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CHAPTER 7-SAS.DOC
TAB7-3.SAS
1The SAS System
1
Analysis Variable : DIF_DEM
N Mean Std Dev Minimum Maximum
----------------------------------------------------------
36 84.8611111 44.2267875 -17.0000000 145.0000000
----------------------------------------------------------
1The SAS System
2
T DEMAND DIF_DEM TREND DETREND COSWT SINWT COS2WT SIN2WT
1 546 . 661.250 -115.250 0.86602 0.50000 0.50000 0.86603
2 578 . 668.322 -90.322 0.50000 0.86603 -0.50000 0.86602
3 660 . 675.393 -15.393 -0.00000 1.00000 -1.00000 -0.00001
4 707 . 682.465 24.535 -0.50000 0.86602 -0.49999 -0.86603
5 738 . 689.537 48.463 -0.86603 0.49999 0.50001 -0.86602
6 781 . 696.609 84.391 -1.00000 -0.00001 1.00000 0.00001
7 848 . 703.681 144.319 -0.86602 -0.50001 0.49999 0.86603
8 818 . 710.752 107.248 -0.49999 -0.86603 -0.50002 0.86602
9 729 . 717.824 11.176 0.00001 -1.00000 -1.00000 -0.00002
10 691 . 724.896 -33.896 0.50001 -0.86602 -0.49998 -0.86604
11 658 . 731.968 -73.968 0.86603 -0.49999 0.50002 -0.86601
12 604 . 739.040 -135.040 1.00000 0.00001 1.00000 0.00003
13 629 83 746.111 -117.111 0.86602 0.50001 0.49997 0.86604
14 711 133 753.183 -42.183 0.49999 0.86603 -0.50003 0.86601
15 729 69 760.255 -31.255 -0.00002 1.00000 -1.00000 -0.00004
16 798 91 767.327 30.673 -0.50002 0.86602 -0.49997 -0.86604
17 861 123 774.399 86.601 -0.86604 0.49998 0.50004 -0.86600
18 903 122 781.470 121.530 -1.00000 -0.00002 1.00000 0.00004
19 968 120 788.542 179.458 -0.86601 -0.50002 0.49996 0.86605
20 894 76 795.614 98.386 -0.49998 -0.86604 -0.50004 0.86600
21 860 131 802.686 57.314 0.00003 -1.00000 -1.00000 -0.00005
22 792 101 809.758 -17.758 0.50002 -0.86601 -0.49995 -0.86605
23 739 81 816.829 -77.829 0.86604 -0.49998 0.50005 -0.86600
24 699 95 823.901 -124.901 1.00000 0.00003 1.00000 0.00006
25 773 144 830.973 -57.973 0.86601 0.50003 0.49995 0.86606
26 818 107 838.045 -20.045 0.49997 0.86604 -0.50006 0.86599
27 871 142 845.117 25.883 -0.00003 1.00000 -1.00000 -0.00007
28 882 84 852.188 29.812 -0.50003 0.86601 -0.49994 -0.86606
29 959 98 859.260 99.740 -0.86604 0.49997 0.50006 -0.86599
30 979 76 866.332 112.668 -1.00000 -0.00004 1.00000 0.00007
31 955 -13 873.404 81.596 -0.86601 -0.50003 0.49993 0.86606
32 925 31 880.476 44.524 -0.49997 -0.86604 -0.50007 0.86599
33 843 -17 887.547 -44.547 0.00004 -1.00000 -1.00000 -0.00008
34 790 -2 894.619 -104.619 0.50004 -0.86600 -0.49993 -0.86607
35 746 7 901.691 -155.691 0.86605 -0.49996 0.50007 -0.86598
36 822 123 908.763 -86.763 1.00000 0.00004 1.00000 0.00009
37 857 84 915.835 -58.835 0.86600 0.50004 0.49992 0.86607
38 876 58 922.906 -46.906 0.49996 0.86605 -0.50008 0.86598
39 959 88 929.978 29.022 -0.00005 1.00000 -1.00000 -0.00010
40 981 99 937.050 43.950 -0.50004 0.86600 -0.49992 -0.86607
41 1051 92 944.122 106.878 -0.86605 0.49996 0.50009 -0.86598
42 1124 145 951.194 172.806 -1.00000 -0.00005 1.00000 0.00010
43 1073 118 958.265 114.735 -0.86600 -0.50005 0.49991 0.86608
44 1020 95 965.337 54.663 -0.49995 -0.86605 -0.50009 0.86597
45 933 90 972.409 -39.409 0.00006 -1.00000 -1.00000 -0.00011
46 787 -3 979.481 -192.481 0.50005 -0.86600 -0.49990 -0.86608
47 830 84 986.553 -156.553 0.86605 -0.49995 0.50010 -0.86597
48 922 100 993.624 -71.624 1.00000 0.00006 1.00000 0.00012
TAB7-3.LIS
1 The SAS System
1
10:58 Monday, February 16,
1998
ARIMA Procedure
Name of variable = PRICE.
Period(s) of Differencing = 1.
Mean of working series = 0.048919
Standard deviation = 0.694919
Number of observations = 99
NOTE: The first observation was eliminated by
differencing.
Autocorrelations
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 0.482912 1.00000 | |********************|
1 -0.034037 -0.07048 | . *| . |
2 -0.040429 -0.08372 | . **| . |
3 -0.014488 -0.03000 | . *| . |
4 0.0046167 0.00956 | . | . |
5 -0.081726 -0.16924 | .***| . |
6 0.042443 0.08789 | . |** . |
7 -0.012038 -0.02493 | . | . |
8 -0.0045294 -0.00938 | . | . |
9 0.064926 0.13445 | . |***. |
10 -0.034838 -0.07214 | . *| . |
11 0.014153 0.02931 | . |* . |
12 -0.0022849 -0.00473 | . | . |
13 -0.013505 -0.02797 | . *| . |
14 0.0045520 0.00943 | . | . |
15 0.0045604 0.00944 | . | . |
16 0.026974 0.05586 | . |* . |
17 0.047961 0.09932 | . |** . |
18 0.025936 0.05371 | . |* . |
19 -0.027323 -0.05658 | . *| . |
20 0.062039 0.12847 | . |***. |
21 -0.051175 -0.10597 | . **| . |
22 -0.0082003 -0.01698 | . | . |
23 0.027657 0.05727 | . |* . |
24 -0.045216 -0.09363 | . **| . |
"." marks two standard errors
1 The SAS System
2
10:58 Monday, February 16,
1998
ARIMA Procedure
Inverse Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 0.01267 | . | . |
2 0.15419 | . |***. |
3 0.14599 | . |***. |
4 -0.07146 | . *| . |
5 0.22274 | . |**** |
6 -0.08706 | . **| . |
7 0.02102 | . | . |
8 0.02252 | . | . |
9 -0.12355 | . **| . |
10 0.05486 | . |* . |
11 -0.05149 | . *| . |
12 -0.03522 | . *| . |
13 -0.02816 | . *| . |
14 -0.04157 | . *| . |
15 -0.07856 | . **| . |
16 -0.08224 | . **| . |
17 -0.10796 | . **| . |
18 -0.09503 | . **| . |
19 0.01959 | . | . |
20 -0.11662 | . **| . |
21 0.05319 | . |* . |
22 -0.00490 | . | . |
23 -0.03944 | . *| . |
24 0.09923 | . |** . |
1 The SAS System
3
10:58 Monday, February 16,
1998
ARIMA Procedure
Partial Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.07048 | . *| . |
2 -0.08913 | . **| . |
3 -0.04327 | . *| . |
4 -0.00370 | . | . |
5 -0.17778 | ****| . |
6 0.06207 | . |* . |
7 -0.04784 | . *| . |
8 -0.01568 | . | . |
9 0.13935 | . |***. |
10 -0.09569 | . **| . |
11 0.07738 | . |** . |
12 -0.02064 | . | . |
13 -0.03160 | . *| . |
14 0.06789 | . |* . |
15 -0.05531 | . *| . |
16 0.11154 | . |** . |
17 0.10076 | . |** . |
18 0.05229 | . |* . |
19 0.02952 | . |* . |
20 0.11983 | . |** . |
21 -0.05539 | . *| . |
22 0.03048 | . |* . |
23 0.05715 | . |* . |
24 -0.11779 | . **| . |
Autocorrelation Check for White Noise
To Chi Autocorrelations
Lag Square DF Prob
6 5.21 6 0.517 -0.070 -0.084 -0.030 0.010 -0.169 0.088
12 7.98 12 0.787 -0.025 -0.009 0.134 -0.072 0.029 -0.005
18 10.03 18 0.931 -0.028 0.009 0.009 0.056 0.099 0.054
24 15.59 24 0.902 -0.057 0.128 -0.106 -0.017 0.057 -0.094
1 The SAS System
4
10:58 Monday, February 16,
1998
ARIMA Procedure
Variance Estimate = 0.48530488
Std Error Estimate = 0.69663827
AIC = 209.375011*
SBC = 209.375011*
Number of Residuals= 99
* Does not include log determinant.
Autocorrelation Check of Residuals
To Chi Autocorrelations
Lag Square DF Prob
6 4.96 6 0.549 -0.066 -0.078 -0.025 0.013 -0.164 0.094
12 7.85 12 0.797 -0.018 -0.003 0.141 -0.067 0.035 0.001
18 10.16 18 0.927 -0.021 0.016 0.014 0.060 0.105 0.060
24 15.60 24 0.902 -0.051 0.134 -0.100 -0.011 0.064 -0.087
Autocorrelation Plot of Residuals
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 0.485305 1.00000 | |********************|
1 -0.031844 -0.06562 | . *| . |
2 -0.037932 -0.07816 | . **| . |
3 -0.012237 -0.02521 | . *| . |
4 0.0063998 0.01319 | . | . |
5 -0.079592 -0.16400 | .***| . |
6 0.045480 0.09371 | . |** . |
7 -0.0088947 -0.01833 | . | . |
8 -0.0015807 -0.00326 | . | . |
9 0.068463 0.14107 | . |***. |
10 -0.032476 -0.06692 | . *| . |
11 0.017104 0.03524 | . |* . |
12 0.00025004 0.00052 | . | . |
13 -0.010290 -0.02120 | . | . |
14 0.0078290 0.01613 | . | . |
15 0.0067834 0.01398 | . | . |
16 0.028920 0.05959 | . |* . |
17 0.050806 0.10469 | . |** . |
18 0.028900 0.05955 | . |* . |
19 -0.024601 -0.05069 | . *| . |
20 0.065228 0.13441 | . |***. |
21 -0.048523 -0.09999 | . **| . |
22 -0.0051529 -0.01062 | . | . |
23 0.030823 0.06351 | . |* . |
24 -0.042109 -0.08677 | . **| . |
"." marks two standard errors
1 The SAS System
5
10:58 Monday, February 16,
1998
ARIMA Procedure
Inverse Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 0.01724 | . | . |
2 0.15794 | . |***. |
3 0.14967 | . |***. |
4 -0.06777 | . *| . |
5 0.22421 | . |**** |
6 -0.08762 | . **| . |
7 0.01846 | . | . |
8 0.01881 | . | . |
9 -0.12964 | .***| . |
10 0.04949 | . |* . |
11 -0.05937 | . *| . |
12 -0.04329 | . *| . |
13 -0.03701 | . *| . |
14 -0.05222 | . *| . |
15 -0.08542 | . **| . |
16 -0.09099 | . **| . |
17 -0.11695 | . **| . |
18 -0.10335 | . **| . |
19 0.00931 | . | . |
20 -0.12303 | . **| . |
21 0.04552 | . |* . |
22 -0.01158 | . | . |
23 -0.04430 | . *| . |
24 0.09358 | . |** . |
1 The SAS System
6
10:58 Monday, February 16,
1998
ARIMA Procedure
Partial Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.06562 | . *| . |
2 -0.08282 | . **| . |
3 -0.03661 | . *| . |
4 0.00227 | . | . |
5 -0.17000 | .***| . |
6 0.07258 | . |* . |
7 -0.03673 | . *| . |
8 -0.00432 | . | . |
9 0.15067 | . |***. |
10 -0.08673 | . **| . |
11 0.08791 | . |** . |
12 -0.01154 | . | . |
13 -0.02078 | . | . |
14 0.07901 | . |** . |
15 -0.04811 | . *| . |
16 0.11901 | . |** . |
17 0.10743 | . |** . |
18 0.05855 | . |* . |
19 0.03648 | . |* . |
20 0.12535 | . |***. |
21 -0.04977 | . *| . |
22 0.03637 | . |* . |
23 0.06238 | . |* . |
24 -0.11190 | . **| . |
Model for variable PRICE
No mean term in this model.
Period(s) of Differencing = 1.
1 The SAS System
7
10:58 Monday, February 16,
1998
ARIMA Procedure
Forecasts for variable PRICE
Obs Forecast Std Error Lower 95% Upper 95%
101 14.8430 0.6966 13.4776 16.2084
102 14.8430 0.9852 12.9121 16.7739
103 14.8430 1.2066 12.4781 17.2079
104 14.8430 1.3933 12.1122 17.5738
105 14.8430 1.5577 11.7899 17.8961
106 14.8430 1.7064 11.4985 18.1875
107 14.8430 1.8431 11.2305 18.4555
108 14.8430 1.9704 10.9811 18.7049
109 14.8430 2.0899 10.7468 18.9392
110 14.8430 2.2030 10.5253 19.1607
111 14.8430 2.3105 10.3145 19.3715
112 14.8430 2.4132 10.1132 19.5728
113 14.8430 2.5118 9.9200 19.7660
114 14.8430 2.6066 9.7342 19.9518
115 14.8430 2.6981 9.5549 20.1311
116 14.8430 2.7866 9.3815 20.3045
117 14.8430 2.8723 9.2134 20.4726
118 14.8430 2.9556 9.0502 20.6358
119 14.8430 3.0366 8.8914 20.7946
120 14.8430 3.1155 8.7368 20.9492
121 14.8430 3.1924 8.5860 21.1000
122 14.8430 3.2675 8.4388 21.2472
123 14.8430 3.3410 8.2948 21.3912
124 14.8430 3.4128 8.1540 21.5320
125 14.8430 3.4832 8.0161 21.6699
126 14.8430 3.5522 7.8809 21.8051
127 14.8430 3.6198 7.7482 21.9378
128 14.8430 3.6863 7.6181 22.0679
129 14.8430 3.7515 7.4902 22.1958
130 14.8430 3.8156 7.3645 22.3215
131 14.8430 3.8787 7.2409 22.4451
132 14.8430 3.9408 7.1192 22.5668
133 14.8430 4.0019 6.9995 22.6865
134 14.8430 4.0621 6.8815 22.8045
135 14.8430 4.1214 6.7653 22.9207
136 14.8430 4.1798 6.6507 23.0353
TAB7-4.SAS
options linesize=80;
data stock;
infile "stocka.dat" obs=100;
input date price;
run;
proc arima;
identify var=price;
run;
proc arima;
identify var=price(1);
estimate noconstant plot;
run;
run;
TAB7-4.LIS
1 The SAS System
1
11:18 Monday, February 16,
1998
ARIMA Procedure
Name of variable = PRICE.
Mean of working series = 15.51685
Standard deviation = 2.647825
Number of observations = 100
Autocorrelations
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 7.010980 1.00000 | |********************|
1 6.616305 0.94371 | . |******************* |
2 6.257471 0.89252 | . |****************** |
3 5.941557 0.84746 | . |***************** |
4 5.675047 0.80945 | . |**************** |
5 5.479436 0.78155 | . |**************** |
6 5.296686 0.75548 | . |*************** |
7 5.015643 0.71540 | . |************** |
8 4.755922 0.67835 | . |************** |
9 4.577116 0.65285 | . |*************. |
10 4.292410 0.61224 | . |************ . |
11 4.102811 0.58520 | . |************ . |
12 3.903485 0.55677 | . |*********** . |
13 3.722051 0.53089 | . |*********** . |
14 3.530595 0.50358 | . |********** . |
15 3.356787 0.47879 | . |********** . |
16 3.221177 0.45945 | . |********* . |
17 3.041688 0.43385 | . |********* . |
18 2.762417 0.39401 | . |******** . |
19 2.420542 0.34525 | . |******* . |
20 2.079820 0.29665 | . |****** . |
21 1.697833 0.24217 | . |***** . |
22 1.380317 0.19688 | . |**** . |
23 1.086652 0.15499 | . |*** . |
24 0.754845 0.10767 | . |** . |
"." marks two standard errors
1 The SAS System
2
11:18 Monday, February 16,
1998
ARIMA Procedure
Inverse Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.49178 | **********| . |
2 -0.05082 | . *| . |
3 0.05354 | . |* . |
4 0.05415 | . |* . |
5 0.00156 | . | . |
6 -0.16998 | .***| . |
7 0.09179 | . |** . |
8 0.14690 | . |***. |
9 -0.26780 | *****| . |
10 0.15280 | . |***. |
11 -0.00688 | . | . |
12 0.03845 | . |* . |
13 -0.09645 | . **| . |
14 0.03447 | . |* . |
15 0.09044 | . |** . |
16 -0.06525 | . *| . |
17 -0.06110 | . *| . |
18 0.04100 | . |* . |
19 0.01974 | . | . |
20 -0.05963 | . *| . |
21 0.02463 | . | . |
22 0.05326 | . |* . |
23 -0.06290 | . *| . |
24 0.03160 | . |* . |
1 The SAS System
3
11:18 Monday, February 16,
1998
ARIMA Procedure
Partial Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 0.94371 | . |******************* |
2 0.01776 | . | . |
3 0.03092 | . |* . |
4 0.04496 | . |* . |
5 0.08046 | . |** . |
6 0.01711 | . | . |
7 -0.12715 | .***| . |
8 0.00876 | . | . |
9 0.08863 | . |** . |
10 -0.15630 | .***| . |
11 0.08570 | . |** . |
12 -0.02070 | . | . |
13 0.03112 | . |* . |
14 -0.04152 | . *| . |
15 -0.00079 | . | . |
16 0.08378 | . |** . |
17 -0.09314 | . **| . |
18 -0.17411 | .***| . |
19 -0.07992 | . **| . |
20 -0.07281 | . *| . |
21 -0.12172 | . **| . |
22 -0.03581 | . *| . |
23 0.01099 | . | . |
24 -0.06675 | . *| . |
Autocorrelation Check for White Noise
To Chi Autocorrelations
Lag Square DF Prob
6 447.32 6 0.000 0.944 0.893 0.847 0.809 0.782 0.755
12 719.91 12 0.000 0.715 0.678 0.653 0.612 0.585 0.557
18 878.61 18 0.000 0.531 0.504 0.479 0.459 0.434 0.394
24 922.22 24 0.000 0.345 0.297 0.242 0.197 0.155 0.108
1 The SAS System
4
11:18 Monday, February 16,
1998
ARIMA Procedure
Name of variable = PRICE.
Period(s) of Differencing = 1.
Mean of working series = 0.048919
Standard deviation = 0.694919
Number of observations = 99
NOTE: The first observation was eliminated by
differencing.
Autocorrelations
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 0.482912 1.00000 | |********************|
1 -0.034037 -0.07048 | . *| . |
2 -0.040429 -0.08372 | . **| . |
3 -0.014488 -0.03000 | . *| . |
4 0.0046167 0.00956 | . | . |
5 -0.081726 -0.16924 | .***| . |
6 0.042443 0.08789 | . |** . |
7 -0.012038 -0.02493 | . | . |
8 -0.0045294 -0.00938 | . | . |
9 0.064926 0.13445 | . |***. |
10 -0.034838 -0.07214 | . *| . |
11 0.014153 0.02931 | . |* . |
12 -0.0022849 -0.00473 | . | . |
13 -0.013505 -0.02797 | . *| . |
14 0.0045520 0.00943 | . | . |
15 0.0045604 0.00944 | . | . |
16 0.026974 0.05586 | . |* . |
17 0.047961 0.09932 | . |** . |
18 0.025936 0.05371 | . |* . |
19 -0.027323 -0.05658 | . *| . |
20 0.062039 0.12847 | . |***. |
21 -0.051175 -0.10597 | . **| . |
22 -0.0082003 -0.01698 | . | . |
23 0.027657 0.05727 | . |* . |
24 -0.045216 -0.09363 | . **| . |
"." marks two standard errors
1 The SAS System
5
11:18 Monday, February 16,
1998
ARIMA Procedure
Inverse Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 0.01267 | . | . |
2 0.15419 | . |***. |
3 0.14599 | . |***. |
4 -0.07146 | . *| . |
5 0.22274 | . |**** |
6 -0.08706 | . **| . |
7 0.02102 | . | . |
8 0.02252 | . | . |
9 -0.12355 | . **| . |
10 0.05486 | . |* . |
11 -0.05149 | . *| . |
12 -0.03522 | . *| . |
13 -0.02816 | . *| . |
14 -0.04157 | . *| . |
15 -0.07856 | . **| . |
16 -0.08224 | . **| . |
17 -0.10796 | . **| . |
18 -0.09503 | . **| . |
19 0.01959 | . | . |
20 -0.11662 | . **| . |
21 0.05319 | . |* . |
22 -0.00490 | . | . |
23 -0.03944 | . *| . |
24 0.09923 | . |** . |
1 The SAS System
6
11:18 Monday, February 16,
1998
ARIMA Procedure
Partial Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.07048 | . *| . |
2 -0.08913 | . **| . |
3 -0.04327 | . *| . |
4 -0.00370 | . | . |
5 -0.17778 | ****| . |
6 0.06207 | . |* . |
7 -0.04784 | . *| . |
8 -0.01568 | . | . |
9 0.13935 | . |***. |
10 -0.09569 | . **| . |
11 0.07738 | . |** . |
12 -0.02064 | . | . |
13 -0.03160 | . *| . |
14 0.06789 | . |* . |
15 -0.05531 | . *| . |
16 0.11154 | . |** . |
17 0.10076 | . |** . |
18 0.05229 | . |* . |
19 0.02952 | . |* . |
20 0.11983 | . |** . |
21 -0.05539 | . *| . |
22 0.03048 | . |* . |
23 0.05715 | . |* . |
24 -0.11779 | . **| . |
Autocorrelation Check for White Noise
To Chi Autocorrelations
Lag Square DF Prob
6 5.21 6 0.517 -0.070 -0.084 -0.030 0.010 -0.169 0.088
12 7.98 12 0.787 -0.025 -0.009 0.134 -0.072 0.029 -0.005
18 10.03 18 0.931 -0.028 0.009 0.009 0.056 0.099 0.054
24 15.59 24 0.902 -0.057 0.128 -0.106 -0.017 0.057 -0.094
1 The SAS System
7
11:18 Monday, February 16,
1998
ARIMA Procedure
Variance Estimate = 0.48530488
Std Error Estimate = 0.69663827
AIC = 209.375011*
SBC = 209.375011*
Number of Residuals= 99
* Does not include log determinant.
Autocorrelation Check of Residuals
To Chi Autocorrelations
Lag Square DF Prob
6 4.96 6 0.549 -0.066 -0.078 -0.025 0.013 -0.164 0.094
12 7.85 12 0.797 -0.018 -0.003 0.141 -0.067 0.035 0.001
18 10.16 18 0.927 -0.021 0.016 0.014 0.060 0.105 0.060
24 15.60 24 0.902 -0.051 0.134 -0.100 -0.011 0.064 -0.087
Autocorrelation Plot of Residuals
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 0.485305 1.00000 | |********************|
1 -0.031844 -0.06562 | . *| . |
2 -0.037932 -0.07816 | . **| . |
3 -0.012237 -0.02521 | . *| . |
4 0.0063998 0.01319 | . | . |
5 -0.079592 -0.16400 | .***| . |
6 0.045480 0.09371 | . |** . |
7 -0.0088947 -0.01833 | . | . |
8 -0.0015807 -0.00326 | . | . |
9 0.068463 0.14107 | . |***. |
10 -0.032476 -0.06692 | . *| . |
11 0.017104 0.03524 | . |* . |
12 0.00025004 0.00052 | . | . |
13 -0.010290 -0.02120 | . | . |
14 0.0078290 0.01613 | . | . |
15 0.0067834 0.01398 | . | . |
16 0.028920 0.05959 | . |* . |
17 0.050806 0.10469 | . |** . |
18 0.028900 0.05955 | . |* . |
19 -0.024601 -0.05069 | . *| . |
20 0.065228 0.13441 | . |***. |
21 -0.048523 -0.09999 | . **| . |
22 -0.0051529 -0.01062 | . | . |
23 0.030823 0.06351 | . |* . |
24 -0.042109 -0.08677 | . **| . |
"." marks two standard errors
1 The SAS System
8
11:18 Monday, February 16,
1998
ARIMA Procedure
Inverse Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 0.01724 | . | . |
2 0.15794 | . |***. |
3 0.14967 | . |***. |
4 -0.06777 | . *| . |
5 0.22421 | . |**** |
6 -0.08762 | . **| . |
7 0.01846 | . | . |
8 0.01881 | . | . |
9 -0.12964 | .***| . |
10 0.04949 | . |* . |
11 -0.05937 | . *| . |
12 -0.04329 | . *| . |
13 -0.03701 | . *| . |
14 -0.05222 | . *| . |
15 -0.08542 | . **| . |
16 -0.09099 | . **| . |
17 -0.11695 | . **| . |
18 -0.10335 | . **| . |
19 0.00931 | . | . |
20 -0.12303 | . **| . |
21 0.04552 | . |* . |
22 -0.01158 | . | . |
23 -0.04430 | . *| . |
24 0.09358 | . |** . |
1 The SAS System
9
11:18 Monday, February 16,
1998
ARIMA Procedure
Partial Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.06562 | . *| . |
2 -0.08282 | . **| . |
3 -0.03661 | . *| . |
4 0.00227 | . | . |
5 -0.17000 | .***| . |
6 0.07258 | . |* . |
7 -0.03673 | . *| . |
8 -0.00432 | . | . |
9 0.15067 | . |***. |
10 -0.08673 | . **| . |
11 0.08791 | . |** . |
12 -0.01154 | . | . |
13 -0.02078 | . | . |
14 0.07901 | . |** . |
15 -0.04811 | . *| . |
16 0.11901 | . |** . |
17 0.10743 | . |** . |
18 0.05855 | . |* . |
19 0.03648 | . |* . |
20 0.12535 | . |***. |
21 -0.04977 | . *| . |
22 0.03637 | . |* . |
23 0.06238 | . |* . |
24 -0.11190 | . **| . |
Model for variable PRICE
No mean term in this model.
Period(s) of Differencing = 1.
TAB7-5.SAS
options linesize=80;
data milk;
infile "dairy.dat" obs=100;
input date sales;
run;
proc arima;
identify var=sales;
run;
run;
TAB7-5.LIS
1 The SAS System
1
11:31 Monday, February 16,
1998
ARIMA Procedure
Name of variable = SALES.
Mean of working series = 199.0239
Standard deviation = 2.883542
Number of observations = 100
Autocorrelations
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 8.314817 1.00000 | |********************|
1 6.223140 0.74844 | . |*************** |
2 4.124599 0.49605 | . |********** |
3 3.081880 0.37065 | . |******* |
4 2.018176 0.24272 | . |***** . |
5 1.251190 0.15048 | . |*** . |
6 0.759899 0.09139 | . |** . |
7 0.707173 0.08505 | . |** . |
8 1.014699 0.12204 | . |** . |
9 1.590408 0.19127 | . |**** . |
10 1.871849 0.22512 | . |***** . |
11 1.329471 0.15989 | . |*** . |
12 0.606646 0.07296 | . |* . |
13 -0.476875 -0.05735 | . *| . |
14 -1.308602 -0.15738 | . ***| . |
15 -1.258037 -0.15130 | . ***| . |
16 -1.425910 -0.17149 | . ***| . |
17 -1.522474 -0.18310 | . ****| . |
18 -1.268607 -0.15257 | . ***| . |
19 -1.083881 -0.13036 | . ***| . |
20 -1.535855 -0.18471 | . ****| . |
21 -1.568480 -0.18864 | . ****| . |
22 -1.624036 -0.19532 | . ****| . |
23 -2.015820 -0.24244 | . *****| . |
24 -1.695036 -0.20386 | . ****| . |
"." marks two standard errors
1 The SAS System
2
11:31 Monday, February 16,
1998
ARIMA Procedure
Inverse Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.63272 | *************| . |
2 0.29916 | . |****** |
3 -0.19995 | ****| . |
4 0.06821 | . |* . |
5 -0.09864 | . **| . |
6 0.07605 | . |** . |
7 0.05355 | . |* . |
8 -0.05483 | . *| . |
9 0.10985 | . |** . |
10 -0.15924 | .***| . |
11 0.03824 | . |* . |
12 -0.01157 | . | . |
13 -0.08220 | . **| . |
14 0.21563 | . |**** |
15 -0.17699 | ****| . |
16 0.14126 | . |***. |
17 -0.12530 | .***| . |
18 0.13684 | . |***. |
19 -0.20936 | ****| . |
20 0.19070 | . |**** |
21 -0.06271 | . *| . |
22 -0.02454 | . | . |
23 0.08539 | . |** . |
24 -0.05516 | . *| . |
1 The SAS System
3
11:31 Monday, February 16,
1998
ARIMA Procedure
Partial Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 0.74844 | . |*************** |
2 -0.14575 | .***| . |
3 0.12627 | . |***. |
4 -0.11905 | . **| . |
5 0.03430 | . |* . |
6 -0.03092 | . *| . |
7 0.09332 | . |** . |
8 0.07645 | . |** . |
9 0.13852 | . |***. |
10 -0.00366 | . | . |
11 -0.13532 | .***| . |
12 -0.07073 | . *| . |
13 -0.20690 | ****| . |
14 -0.01038 | . | . |
15 0.10165 | . |** . |
16 -0.08523 | . **| . |
17 0.00147 | . | . |
18 -0.04400 | . *| . |
19 -0.07247 | . *| . |
20 -0.21481 | ****| . |
21 0.12219 | . |** . |
22 -0.07255 | . *| . |
23 0.02764 | . |* . |
24 0.12866 | . |***. |
Autocorrelation Check for White Noise
To Chi Autocorrelations
Lag Square DF Prob
6 107.37 6 0.000 0.748 0.496 0.371 0.243 0.150 0.091
12 123.20 12 0.000 0.085 0.122 0.191 0.225 0.160 0.073
18 139.86 18 0.000 -0.057 -0.157 -0.151 -0.171 -0.183 -0.153
24 169.30 24 0.000 -0.130 -0.185 -0.189 -0.195 -0.242 -0.204
TAB7-6.SAS
OPTION LINESIZE=80;
DATA DAIRY;
INFILE DAIRY;
INPUT TIME SALES;
PROC ARIMA;
IDENTIFY VAR=SALES;
ESTIMATE P=1 PLOT;
FORECAST OUT=B1 BACK=0 LEAD=36;
TAB7-6.LIS
1 The SAS System
1
14:41 Monday, April 6,
1998
ARIMA Procedure
Name of variable = SALES.
Mean of working series = 199.0239
Standard deviation = 2.883542
Number of observations = 100
Autocorrelations
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 8.314817 1.00000 | |********************|
1 6.223140 0.74844 | . |*************** |
2 4.124599 0.49605 | . |********** |
3 3.081880 0.37065 | . |******* |
4 2.018176 0.24272 | . |***** . |
5 1.251190 0.15048 | . |*** . |
6 0.759899 0.09139 | . |** . |
7 0.707173 0.08505 | . |** . |
8 1.014699 0.12204 | . |** . |
9 1.590408 0.19127 | . |**** . |
10 1.871849 0.22512 | . |***** . |
11 1.329471 0.15989 | . |*** . |
12 0.606646 0.07296 | . |* . |
13 -0.476875 -0.05735 | . *| . |
14 -1.308602 -0.15738 | . ***| . |
15 -1.258037 -0.15130 | . ***| . |
16 -1.425910 -0.17149 | . ***| . |
17 -1.522474 -0.18310 | . ****| . |
18 -1.268607 -0.15257 | . ***| . |
19 -1.083881 -0.13036 | . ***| . |
20 -1.535855 -0.18471 | . ****| . |
21 -1.568480 -0.18864 | . ****| . |
22 -1.624036 -0.19532 | . ****| . |
23 -2.015820 -0.24244 | . *****| . |
24 -1.695036 -0.20386 | . ****| . |
"." marks two standard errors
1 The SAS System
2
14:41 Monday, April 6,
1998
ARIMA Procedure
Inverse Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.63272 | *************| . |
2 0.29916 | . |****** |
3 -0.19995 | ****| . |
4 0.06821 | . |* . |
5 -0.09864 | . **| . |
6 0.07605 | . |** . |
7 0.05355 | . |* . |
8 -0.05483 | . *| . |
9 0.10985 | . |** . |
10 -0.15924 | .***| . |
11 0.03824 | . |* . |
12 -0.01157 | . | . |
13 -0.08220 | . **| . |
14 0.21563 | . |**** |
15 -0.17699 | ****| . |
16 0.14126 | . |***. |
17 -0.12530 | .***| . |
18 0.13684 | . |***. |
19 -0.20936 | ****| . |
20 0.19070 | . |**** |
21 -0.06271 | . *| . |
22 -0.02454 | . | . |
23 0.08539 | . |** . |
24 -0.05516 | . *| . |
1 The SAS System
3
14:41 Monday, April 6,
1998
ARIMA Procedure
Partial Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 0.74844 | . |*************** |
2 -0.14575 | .***| . |
3 0.12627 | . |***. |
4 -0.11905 | . **| . |
5 0.03430 | . |* . |
6 -0.03092 | . *| . |
7 0.09332 | . |** . |
8 0.07645 | . |** . |
9 0.13852 | . |***. |
10 -0.00366 | . | . |
11 -0.13532 | .***| . |
12 -0.07073 | . *| . |
13 -0.20690 | ****| . |
14 -0.01038 | . | . |
15 0.10165 | . |** . |
16 -0.08523 | . **| . |
17 0.00147 | . | . |
18 -0.04400 | . *| . |
19 -0.07247 | . *| . |
20 -0.21481 | ****| . |
21 0.12219 | . |** . |
22 -0.07255 | . *| . |
23 0.02764 | . |* . |
24 0.12866 | . |***. |
Autocorrelation Check for White Noise
To Chi Autocorrelations
Lag Square DF Prob
6 107.37 6 0.000 0.748 0.496 0.371 0.243 0.150 0.091
12 123.20 12 0.000 0.085 0.122 0.191 0.225 0.160 0.073
18 139.86 18 0.000 -0.057 -0.157 -0.151 -0.171 -0.183 -0.153
24 169.30 24 0.000 -0.130 -0.185 -0.189 -0.195 -0.242 -0.204
1 The SAS System
4
14:41 Monday, April 6,
1998
ARIMA Procedure
Conditional Least Squares Estimation
Approx.
Parameter Estimate Std Error T Ratio Lag
MU 199.21741 0.72813 273.60 0
AR1,1 0.75343 0.06690 11.26 1
Constant Estimate = 49.1207118
Variance Estimate = 3.70480268
Std Error Estimate = 1.9247864
AIC = 416.730436*
SBC = 421.940776*
Number of Residuals= 100
* Does not include log determinant.
Correlations of the Estimates
Parameter MU AR1,1
MU 1.000 0.068
AR1,1 0.068 1.000
Autocorrelation Check of Residuals
To Chi Autocorrelations
Lag Square DF Prob
6 4.88 5 0.431 0.111 -0.148 0.063 -0.029 -0.036 -0.079
12 12.44 11 0.332 -0.050 -0.049 0.077 0.205 0.068 0.096
18 19.05 17 0.326 -0.057 -0.203 0.036 -0.035 -0.091 -0.009
24 26.19 23 0.292 0.098 -0.109 -0.025 0.048 -0.170 -0.038
1 The SAS System
5
14:41 Monday, April 6,
1998
ARIMA Procedure
Autocorrelation Plot of Residuals
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 3.704803 1.00000 | |********************|
1 0.412227 0.11127 | . |** . |
2 -0.549526 -0.14833 | .***| . |
3 0.232035 0.06263 | . |* . |
4 -0.109171 -0.02947 | . *| . |
5 -0.133847 -0.03613 | . *| . |
6 -0.291249 -0.07861 | . **| . |
7 -0.183977 -0.04966 | . *| . |
8 -0.181248 -0.04892 | . *| . |
9 0.284563 0.07681 | . |** . |
10 0.759857 0.20510 | . |**** |
11 0.252521 0.06816 | . |* . |
12 0.354407 0.09566 | . |** . |
13 -0.211304 -0.05704 | . *| . |
14 -0.753198 -0.20330 | ****| . |
15 0.132048 0.03564 | . |* . |
16 -0.130727 -0.03529 | . *| . |
17 -0.336384 -0.09080 | . **| . |
18 -0.034250 -0.00924 | . | . |
19 0.361320 0.09753 | . |** . |
20 -0.405210 -0.10937 | . **| . |
21 -0.094030 -0.02538 | . *| . |
22 0.176919 0.04775 | . |* . |
23 -0.630965 -0.17031 | . ***| . |
24 -0.140654 -0.03797 | . *| . |
"." marks two standard errors
1 The SAS System
6
14:41 Monday, April 6,
1998
ARIMA Procedure
Inverse Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.16698 | .***| . |
2 0.21648 | . |**** |
3 -0.16153 | .***| . |
4 -0.02026 | . | . |
5 -0.07243 | . *| . |
6 0.12148 | . |** . |
7 0.09324 | . |** . |
8 0.01978 | . | . |
9 0.01701 | . | . |
10 -0.21381 | ****| . |
11 -0.10494 | . **| . |
12 -0.04447 | . *| . |
13 -0.03740 | . *| . |
14 0.22994 | . |***** |
15 -0.06730 | . *| . |
16 0.10634 | . |** . |
17 -0.07234 | . *| . |
18 0.06665 | . |* . |
19 -0.11030 | . **| . |
20 0.16574 | . |***. |
21 0.03548 | . |* . |
22 0.02524 | . |* . |
23 0.10585 | . |** . |
24 -0.04879 | . *| . |
1 The SAS System
7
14:41 Monday, April 6,
1998
ARIMA Procedure
Partial Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 0.11127 | . |** . |
2 -0.16272 | .***| . |
3 0.10393 | . |** . |
4 -0.08025 | . **| . |
5 0.00681 | . | . |
6 -0.10454 | . **| . |
7 -0.02078 | . | . |
8 -0.07403 | . *| . |
9 0.10248 | . |** . |
10 0.16682 | . |***. |
11 0.05633 | . |* . |
12 0.12827 | . |***. |
13 -0.11279 | . **| . |
14 -0.16472 | .***| . |
15 0.05204 | . |* . |
16 -0.05878 | . *| . |
17 0.00502 | . | . |
18 0.00335 | . | . |
19 0.08163 | . |** . |
20 -0.23480 | *****| . |
21 -0.00047 | . | . |
22 -0.10039 | . **| . |
23 -0.12324 | . **| . |
24 0.06552 | . |* . |
Model for variable SALES
Estimated Mean = 199.217408
Autoregressive Factors
Factor 1: 1 - 0.75343 B**(1)
1 The SAS System
8
14:41 Monday, April 6,
1998
ARIMA Procedure
Forecasts for variable SALES
Obs Forecast Std Error Lower 95% Upper 95%
101 200.6223 1.9248 196.8497 204.3948
102 200.2759 2.4100 195.5524 204.9993
103 200.0149 2.6461 194.8287 205.2011
104 199.8182 2.7712 194.3869 205.2496
105 199.6701 2.8397 194.1043 205.2359
106 199.5585 2.8779 193.9179 205.1991
107 199.4744 2.8994 193.7917 205.1571
108 199.4110 2.9115 193.7046 205.1174
109 199.3633 2.9183 193.6434 205.0831
110 199.3273 2.9222 193.5999 205.0548
111 199.3002 2.9244 193.5684 205.0320
112 199.2798 2.9257 193.5456 205.0140
113 199.2644 2.9264 193.5288 205.0000
114 199.2528 2.9268 193.5164 204.9892
115 199.2441 2.9270 193.5072 204.9809
116 199.2375 2.9271 193.5004 204.9746
117 199.2326 2.9272 193.4953 204.9698
118 199.2288 2.9273 193.4915 204.9661
119 199.2260 2.9273 193.4886 204.9634
120 199.2239 2.9273 193.4865 204.9613
121 199.2223 2.9273 193.4849 204.9597
122 199.2211 2.9273 193.4837 204.9585
123 199.2202 2.9273 193.4828 204.9576
124 199.2195 2.9273 193.4821 204.9569
125 199.2190 2.9273 193.4816 204.9564
126 199.2186 2.9273 193.4812 204.9560
127 199.2183 2.9273 193.4809 204.9557
128 199.2181 2.9273 193.4806 204.9555
129 199.2179 2.9273 193.4805 204.9553
130 199.2178 2.9273 193.4804 204.9552
131 199.2177 2.9273 193.4803 204.9551
132 199.2176 2.9273 193.4802 204.9551
133 199.2176 2.9273 193.4801 204.9550
134 199.2175 2.9273 193.4801 204.9550
135 199.2175 2.9273 193.4801 204.9549
136 199.2175 2.9273 193.4800 204.9549
TAB7-7.SAS
options linesize=80;
data dairy;
infile "dairy.dat" obs=100;
input date sales;
run;
proc arima;
identify var=sales noprint;
estimate p=1 plot;
run;
run;
TAB7-7.LIS
1 The SAS System
1
12:35 Monday, February 16,
1998
ARIMA Procedure
Conditional Least Squares Estimation
Approx.
Parameter Estimate Std Error T Ratio Lag
MU 199.21741 0.72813 273.60 0
AR1,1 0.75343 0.06690 11.26 1
Constant Estimate = 49.1207118
Variance Estimate = 3.70480268
Std Error Estimate = 1.9247864
AIC = 416.730436*
SBC = 421.940776*
Number of Residuals= 100
* Does not include log determinant.
Correlations of the Estimates
Parameter MU AR1,1
MU 1.000 0.068
AR1,1 0.068 1.000
Autocorrelation Check of Residuals
To Chi Autocorrelations
Lag Square DF Prob
6 4.88 5 0.431 0.111 -0.148 0.063 -0.029 -0.036 -0.079
12 12.44 11 0.332 -0.050 -0.049 0.077 0.205 0.068 0.096
18 19.05 17 0.326 -0.057 -0.203 0.036 -0.035 -0.091 -0.009
24 26.19 23 0.292 0.098 -0.109 -0.025 0.048 -0.170 -0.038
1 The SAS System
2
12:35 Monday, February 16,
1998
ARIMA Procedure
Autocorrelation Plot of Residuals
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 3.704803 1.00000 | |********************|
1 0.412227 0.11127 | . |** . |
2 -0.549526 -0.14833 | .***| . |
3 0.232035 0.06263 | . |* . |
4 -0.109171 -0.02947 | . *| . |
5 -0.133847 -0.03613 | . *| . |
6 -0.291249 -0.07861 | . **| . |
7 -0.183977 -0.04966 | . *| . |
8 -0.181248 -0.04892 | . *| . |
9 0.284563 0.07681 | . |** . |
10 0.759857 0.20510 | . |**** |
11 0.252521 0.06816 | . |* . |
12 0.354407 0.09566 | . |** . |
13 -0.211304 -0.05704 | . *| . |
14 -0.753198 -0.20330 | ****| . |
15 0.132048 0.03564 | . |* . |
16 -0.130727 -0.03529 | . *| . |
17 -0.336384 -0.09080 | . **| . |
18 -0.034250 -0.00924 | . | . |
19 0.361320 0.09753 | . |** . |
20 -0.405210 -0.10937 | . **| . |
21 -0.094030 -0.02538 | . *| . |
22 0.176919 0.04775 | . |* . |
23 -0.630965 -0.17031 | . ***| . |
24 -0.140654 -0.03797 | . *| . |
"." marks two standard errors
1 The SAS System
3
12:35 Monday, February 16,
1998
ARIMA Procedure
Inverse Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.16698 | .***| . |
2 0.21648 | . |**** |
3 -0.16153 | .***| . |
4 -0.02026 | . | . |
5 -0.07243 | . *| . |
6 0.12148 | . |** . |
7 0.09324 | . |** . |
8 0.01978 | . | . |
9 0.01701 | . | . |
10 -0.21381 | ****| . |
11 -0.10494 | . **| . |
12 -0.04447 | . *| . |
13 -0.03740 | . *| . |
14 0.22994 | . |***** |
15 -0.06730 | . *| . |
16 0.10634 | . |** . |
17 -0.07234 | . *| . |
18 0.06665 | . |* . |
19 -0.11030 | . **| . |
20 0.16574 | . |***. |
21 0.03548 | . |* . |
22 0.02524 | . |* . |
23 0.10585 | . |** . |
24 -0.04879 | . *| . |
1 The SAS System
4
12:35 Monday, February 16,
1998
ARIMA Procedure
Partial Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 0.11127 | . |** . |
2 -0.16272 | .***| . |
3 0.10393 | . |** . |
4 -0.08025 | . **| . |
5 0.00681 | . | . |
6 -0.10454 | . **| . |
7 -0.02078 | . | . |
8 -0.07403 | . *| . |
9 0.10248 | . |** . |
10 0.16682 | . |***. |
11 0.05633 | . |* . |
12 0.12827 | . |***. |
13 -0.11279 | . **| . |
14 -0.16472 | .***| . |
15 0.05204 | . |* . |
16 -0.05878 | . *| . |
17 0.00502 | . | . |
18 0.00335 | . | . |
19 0.08163 | . |** . |
20 -0.23480 | *****| . |
21 -0.00047 | . | . |
22 -0.10039 | . **| . |
23 -0.12324 | . **| . |
24 0.06552 | . |* . |
Model for variable SALES
Estimated Mean = 199.217408
Autoregressive Factors
Factor 1: 1 - 0.75343 B**(1)
TAB7-8.SAS
options linesize=80;
data fad;
infile "fad.dat" obs=100;
input demand;
run;
proc arima;
identify var=demand;
run;
run;
TAB7-8.LIS
1 The SAS System
1
12:43 Monday, February 16,
1998
ARIMA Procedure
Name of variable = DEMAND.
Mean of working series = 12.8703
Standard deviation = 3.584918
Number of observations = 100
Autocorrelations
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 12.851635 1.00000 | |********************|
1 11.629775 0.90493 | . |****************** |
2 10.945612 0.85169 | . |***************** |
3 10.362472 0.80632 | . |**************** |
4 9.811327 0.76343 | . |*************** |
5 9.254384 0.72009 | . |************** |
6 8.834901 0.68745 | . |************** |
7 8.166477 0.63544 | . |************* |
8 7.635316 0.59411 | . |************ |
9 7.317404 0.56938 | . |*********** . |
10 6.786961 0.52810 | . |*********** . |
11 6.310901 0.49106 | . |********** . |
12 5.899553 0.45905 | . |********* . |
13 5.369709 0.41782 | . |******** . |
14 4.994137 0.38860 | . |******** . |
15 4.716024 0.36696 | . |******* . |
16 4.396404 0.34209 | . |******* . |
17 3.827135 0.29779 | . |****** . |
18 3.278354 0.25509 | . |***** . |
19 2.605434 0.20273 | . |**** . |
20 1.962068 0.15267 | . |*** . |
21 1.238614 0.09638 | . |** . |
22 0.597369 0.04648 | . |* . |
23 0.107626 0.00837 | . | . |
24 -0.557477 -0.04338 | . *| . |
"." marks two standard errors
1 The SAS System
2
12:43 Monday, February 16,
1998
ARIMA Procedure
Inverse Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.40157 | ********| . |
2 -0.07525 | . **| . |
3 0.01835 | . | . |
4 -0.03887 | . *| . |
5 0.04918 | . |* . |
6 -0.11770 | . **| . |
7 0.07305 | . |* . |
8 0.06826 | . |* . |
9 -0.11356 | . **| . |
10 0.03208 | . |* . |
11 0.03069 | . |* . |
12 -0.05952 | . *| . |
13 0.04022 | . |* . |
14 0.05813 | . |* . |
15 -0.00646 | . | . |
16 -0.09915 | . **| . |
17 0.04887 | . |* . |
18 -0.03147 | . *| . |
19 0.02050 | . | . |
20 -0.04856 | . *| . |
21 0.03997 | . |* . |
22 0.07105 | . |* . |
23 -0.11716 | . **| . |
24 0.06402 | . |* . |
1 The SAS System
3
12:43 Monday, February 16,
1998
ARIMA Procedure
Partial Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 0.90493 | . |****************** |
2 0.18110 | . |**** |
3 0.06447 | . |* . |
4 0.01970 | . | . |
5 -0.00941 | . | . |
6 0.04241 | . |* . |
7 -0.10137 | . **| . |
8 -0.00254 | . | . |
9 0.07842 | . |** . |
10 -0.06793 | . *| . |
11 -0.01541 | . | . |
12 -0.00072 | . | . |
13 -0.05433 | . *| . |
14 0.02924 | . |* . |
15 0.02449 | . | . |
16 0.00911 | . | . |
17 -0.11965 | . **| . |
18 -0.08380 | . **| . |
19 -0.09328 | . **| . |
20 -0.07105 | . *| . |
21 -0.10587 | . **| . |
22 -0.02986 | . *| . |
23 0.04342 | . |* . |
24 -0.10449 | . **| . |
Autocorrelation Check for White Noise
To Chi Autocorrelations
Lag Square DF Prob
6 397.12 6 0.000 0.905 0.852 0.806 0.763 0.720 0.687
12 600.54 12 0.000 0.635 0.594 0.569 0.528 0.491 0.459
18 688.28 18 0.000 0.418 0.389 0.367 0.342 0.298 0.255
24 698.17 24 0.000 0.203 0.153 0.096 0.046 0.008 -0.043
TAB7-9.SAS
options linesize=80;
data fad;
infile "fad.dat" obs=100;
input demand;
run;
proc arima;
identify var=demand(1) noprint;
estimate noconstant plot;
run;
run;
TAB7-9.LIS
1 The SAS System
1
12:52 Monday, February 16,
1998
ARIMA Procedure
Variance Estimate = 1.72893838
Std Error Estimate = 1.31489102
AIC = 335.153079*
SBC = 335.153079*
Number of Residuals= 99
* Does not include log determinant.
Autocorrelation Check of Residuals
To Chi Autocorrelations
Lag Square DF Prob
6 20.29 6 0.002 -0.347 -0.007 0.007 0.088 -0.182 0.185
12 25.53 12 0.012 -0.055 -0.022 0.167 -0.106 0.064 0.021
18 27.34 18 0.073 -0.046 0.048 -0.015 0.050 0.046 0.076
24 37.47 24 0.039 -0.118 0.187 -0.123 -0.001 0.084 -0.092
Autocorrelation Plot of Residuals
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 1.728938 1.00000 | |********************|
1 -0.599675 -0.34685 | *******| . |
2 -0.012016 -0.00695 | . | . |
3 0.011262 0.00651 | . | . |
4 0.152834 0.08840 | . |** . |
5 -0.313826 -0.18151 | .****| . |
6 0.319639 0.18488 | . |****. |
7 -0.094366 -0.05458 | . *| . |
8 -0.037745 -0.02183 | . | . |
9 0.288487 0.16686 | . |*** . |
10 -0.183449 -0.10611 | . **| . |
11 0.110165 0.06372 | . |* . |
12 0.036532 0.02113 | . | . |
13 -0.079672 -0.04608 | . *| . |
14 0.083380 0.04823 | . |* . |
15 -0.026404 -0.01527 | . | . |
16 0.086163 0.04984 | . |* . |
17 0.079812 0.04616 | . |* . |
18 0.130592 0.07553 | . |** . |
19 -0.203259 -0.11756 | . **| . |
20 0.322646 0.18662 | . |****. |
21 -0.212183 -0.12272 | . **| . |
22 -0.0019545 -0.00113 | . | . |
23 0.144367 0.08350 | . |** . |
24 -0.159786 -0.09242 | . **| . |
"." marks two standard errors
1 The SAS System
2
12:52 Monday, February 16,
1998
ARIMA Procedure
Inverse Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 0.35890 | . |******* |
2 0.24559 | . |***** |
3 0.13768 | . |***. |
4 -0.02584 | . *| . |
5 0.11583 | . |** . |
6 -0.10149 | . **| . |
7 -0.03582 | . *| . |
8 -0.05335 | . *| . |
9 -0.12793 | .***| . |
10 -0.01619 | . | . |
11 -0.07486 | . *| . |
12 -0.05031 | . *| . |
13 -0.05763 | . *| . |
14 -0.08195 | . **| . |
15 -0.12228 | . **| . |
16 -0.15967 | .***| . |
17 -0.15585 | .***| . |
18 -0.14294 | .***| . |
19 -0.04231 | . *| . |
20 -0.08689 | . **| . |
21 0.03066 | . |* . |
22 0.03493 | . |* . |
23 0.01940 | . | . |
24 0.08783 | . |** . |
1 The SAS System
3
12:52 Monday, February 16,
1998
ARIMA Procedure
Partial Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.34685 | *******| . |
2 -0.14465 | .***| . |
3 -0.05389 | . *| . |
4 0.08289 | . |** . |
5 -0.13662 | .***| . |
6 0.09684 | . |** . |
7 0.02672 | . |* . |
8 -0.01694 | . | . |
9 0.20258 | . |**** |
10 -0.02621 | . *| . |
11 0.10196 | . |** . |
12 0.05724 | . |* . |
13 -0.04861 | . *| . |
14 0.10617 | . |** . |
15 -0.06955 | . *| . |
16 0.09142 | . |** . |
17 0.10283 | . |** . |
18 0.08917 | . |** . |
19 0.02236 | . | . |
20 0.12023 | . |** . |
21 -0.00842 | . | . |
22 -0.02914 | . *| . |
23 0.06199 | . |* . |
24 -0.12051 | . **| . |
Model for variable DEMAND
No mean term in this model.
Period(s) of Differencing = 1.
TAB7-10.SAS
OPTION LINESIZE=80;
DATA FAD;
INFILE FAD;
INPUT SALES;
PROC ARIMA;
IDENTIFY VAR=SALES(1);
ESTIMATE NOCONSTANT PLOT;
FORECAST OUT=B1 BACK=0 LEAD=36;
TAB7-10.LIS
1 The SAS System
1
14:41 Monday, April 6,
1998
ARIMA Procedure
Name of variable = SALES.
Period(s) of Differencing = 1.
Mean of working series = 0.052424
Standard deviation = 1.313846
Number of observations = 99
NOTE: The first observation was eliminated by
differencing.
Autocorrelations
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 1.726190 1.00000 | |********************|
1 -0.602991 -0.34932 | *******| . |
2 -0.014746 -0.00854 | . | . |
3 0.0079905 0.00463 | . | . |
4 0.149170 0.08642 | . |** . |
5 -0.316581 -0.18340 | .****| . |
6 0.318011 0.18423 | . |****. |
7 -0.096487 -0.05590 | . *| . |
8 -0.040276 -0.02333 | . | . |
9 0.287988 0.16683 | . |*** . |
10 -0.186751 -0.10819 | . **| . |
11 0.108631 0.06293 | . |* . |
12 0.033949 0.01967 | . | . |
13 -0.081012 -0.04693 | . *| . |
14 0.082462 0.04777 | . |* . |
15 -0.028764 -0.01666 | . | . |
16 0.083399 0.04831 | . |* . |
17 0.078795 0.04565 | . |* . |
18 0.129775 0.07518 | . |** . |
19 -0.205131 -0.11883 | . **| . |
20 0.321816 0.18643 | . |****. |
21 -0.214211 -0.12409 | . **| . |
22 -0.0031001 -0.00180 | . | . |
23 0.143267 0.08300 | . |** . |
24 -0.160611 -0.09304 | . **| . |
"." marks two standard errors
1 The SAS System
2
14:41 Monday, April 6,
1998
ARIMA Procedure
Inverse Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 0.36477 | . |******* |
2 0.25258 | . |***** |
3 0.14517 | . |***. |
4 -0.01850 | . | . |
5 0.12033 | . |** . |
6 -0.09729 | . **| . |
7 -0.03350 | . *| . |
8 -0.05190 | . *| . |
9 -0.12722 | .***| . |
10 -0.01660 | . | . |
11 -0.07588 | . **| . |
12 -0.05237 | . *| . |
13 -0.06055 | . *| . |
14 -0.08527 | . **| . |
15 -0.12437 | . **| . |
16 -0.16155 | .***| . |
17 -0.15807 | .***| . |
18 -0.14523 | .***| . |
19 -0.04546 | . *| . |
20 -0.08854 | . **| . |
21 0.02834 | . |* . |
22 0.03306 | . |* . |
23 0.01826 | . | . |
24 0.08628 | . |** . |
1 The SAS System
3
14:41 Monday, April 6,
1998
ARIMA Procedure
Partial Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.34932 | *******| . |
2 -0.14871 | .***| . |
3 -0.05911 | . *| . |
4 0.07737 | . |** . |
5 -0.14208 | .***| . |
6 0.09208 | . |** . |
7 0.02320 | . | . |
8 -0.02057 | . | . |
9 0.20102 | . |**** |
10 -0.02794 | . *| . |
11 0.10093 | . |** . |
12 0.05634 | . |* . |
13 -0.04926 | . *| . |
14 0.10685 | . |** . |
15 -0.07045 | . *| . |
16 0.09031 | . |** . |
17 0.10260 | . |** . |
18 0.08986 | . |** . |
19 0.02422 | . | . |
20 0.12204 | . |** . |
21 -0.00634 | . | . |
22 -0.02735 | . *| . |
23 0.06334 | . |* . |
24 -0.11907 | . **| . |
Autocorrelation Check for White Noise
To Chi Autocorrelations
Lag Square DF Prob
6 20.47 6 0.002 -0.349 -0.009 0.005 0.086 -0.183 0.184
12 25.77 12 0.012 -0.056 -0.023 0.167 -0.108 0.063 0.020
18 27.56 18 0.069 -0.047 0.048 -0.017 0.048 0.046 0.075
24 37.76 24 0.037 -0.119 0.186 -0.124 -0.002 0.083 -0.093
1 The SAS System
4
14:41 Monday, April 6,
1998
ARIMA Procedure
Variance Estimate = 1.72893838
Std Error Estimate = 1.31489102
AIC = 335.153079*
SBC = 335.153079*
Number of Residuals= 99
* Does not include log determinant.
Autocorrelation Check of Residuals
To Chi Autocorrelations
Lag Square DF Prob
6 20.29 6 0.002 -0.347 -0.007 0.007 0.088 -0.182 0.185
12 25.53 12 0.012 -0.055 -0.022 0.167 -0.106 0.064 0.021
18 27.34 18 0.073 -0.046 0.048 -0.015 0.050 0.046 0.076
24 37.47 24 0.039 -0.118 0.187 -0.123 -0.001 0.084 -0.092
Autocorrelation Plot of Residuals
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 1.728938 1.00000 | |********************|
1 -0.599675 -0.34685 | *******| . |
2 -0.012016 -0.00695 | . | . |
3 0.011262 0.00651 | . | . |
4 0.152834 0.08840 | . |** . |
5 -0.313826 -0.18151 | .****| . |
6 0.319639 0.18488 | . |****. |
7 -0.094366 -0.05458 | . *| . |
8 -0.037745 -0.02183 | . | . |
9 0.288487 0.16686 | . |*** . |
10 -0.183449 -0.10611 | . **| . |
11 0.110165 0.06372 | . |* . |
12 0.036532 0.02113 | . | . |
13 -0.079672 -0.04608 | . *| . |
14 0.083380 0.04823 | . |* . |
15 -0.026404 -0.01527 | . | . |
16 0.086163 0.04984 | . |* . |
17 0.079812 0.04616 | . |* . |
18 0.130592 0.07553 | . |** . |
19 -0.203259 -0.11756 | . **| . |
20 0.322646 0.18662 | . |****. |
21 -0.212183 -0.12272 | . **| . |
22 -0.0019545 -0.00113 | . | . |
23 0.144367 0.08350 | . |** . |
24 -0.159786 -0.09242 | . **| . |
"." marks two standard errors
1 The SAS System
5
14:41 Monday, April 6,
1998
ARIMA Procedure
Inverse Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 0.35890 | . |******* |
2 0.24559 | . |***** |
3 0.13768 | . |***. |
4 -0.02584 | . *| . |
5 0.11583 | . |** . |
6 -0.10149 | . **| . |
7 -0.03582 | . *| . |
8 -0.05335 | . *| . |
9 -0.12793 | .***| . |
10 -0.01619 | . | . |
11 -0.07486 | . *| . |
12 -0.05031 | . *| . |
13 -0.05763 | . *| . |
14 -0.08195 | . **| . |
15 -0.12228 | . **| . |
16 -0.15967 | .***| . |
17 -0.15585 | .***| . |
18 -0.14294 | .***| . |
19 -0.04231 | . *| . |
20 -0.08689 | . **| . |
21 0.03066 | . |* . |
22 0.03493 | . |* . |
23 0.01940 | . | . |
24 0.08783 | . |** . |
1 The SAS System
6
14:41 Monday, April 6,
1998
ARIMA Procedure
Partial Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.34685 | *******| . |
2 -0.14465 | .***| . |
3 -0.05389 | . *| . |
4 0.08289 | . |** . |
5 -0.13662 | .***| . |
6 0.09684 | . |** . |
7 0.02672 | . |* . |
8 -0.01694 | . | . |
9 0.20258 | . |**** |
10 -0.02621 | . *| . |
11 0.10196 | . |** . |
12 0.05724 | . |* . |
13 -0.04861 | . *| . |
14 0.10617 | . |** . |
15 -0.06955 | . *| . |
16 0.09142 | . |** . |
17 0.10283 | . |** . |
18 0.08917 | . |** . |
19 0.02236 | . | . |
20 0.12023 | . |** . |
21 -0.00842 | . | . |
22 -0.02914 | . *| . |
23 0.06199 | . |* . |
24 -0.12051 | . **| . |
Model for variable SALES
No mean term in this model.
Period(s) of Differencing = 1.
1 The SAS System
7
14:41 Monday, April 6,
1998
ARIMA Procedure
Forecasts for variable SALES
Obs Forecast Std Error Lower 95% Upper 95%
101 10.0000 1.3149 7.4229 12.5771
102 10.0000 1.8595 6.3554 13.6446
103 10.0000 2.2775 5.5363 14.4637
104 10.0000 2.6298 4.8457 15.1543
105 10.0000 2.9402 4.2373 15.7627
106 10.0000 3.2208 3.6873 16.3127
107 10.0000 3.4789 3.1815 16.8185
108 10.0000 3.7191 2.7108 17.2892
109 10.0000 3.9447 2.2686 17.7314
110 10.0000 4.1581 1.8504 18.1496
111 10.0000 4.3610 1.4526 18.5474
112 10.0000 4.5549 1.0725 18.9275
113 10.0000 4.7409 0.7080 19.2920
114 10.0000 4.9199 0.3572 19.6428
115 10.0000 5.0926 0.0188 19.9812
116 10.0000 5.2596 -0.3086 20.3086
117 10.0000 5.4214 -0.6258 20.6258
118 10.0000 5.5786 -0.9339 20.9339
119 10.0000 5.7315 -1.2335 21.2335
120 10.0000 5.8804 -1.5253 21.5253
121 10.0000 6.0256 -1.8099 21.8099
122 10.0000 6.1674 -2.0879 22.0879
123 10.0000 6.3060 -2.3595 22.3595
124 10.0000 6.4416 -2.6254 22.6254
125 10.0000 6.5745 -2.8857 22.8857
126 10.0000 6.7047 -3.1409 23.1409
127 10.0000 6.8324 -3.3912 23.3912
128 10.0000 6.9577 -3.6369 23.6369
129 10.0000 7.0809 -3.8783 23.8783
130 10.0000 7.2020 -4.1156 24.1156
131 10.0000 7.3210 -4.3489 24.3489
132 10.0000 7.4381 -4.5785 24.5785
133 10.0000 7.5535 -4.8045 24.8045
134 10.0000 7.6671 -5.0272 25.0272
135 10.0000 7.7790 -5.2466 25.2466
136 10.0000 7.8893 -5.4628 25.4628
TAB7-11.SAS
OPTION LINESIZE=80;
DATA FAD;
INFILE FAD;
INPUT SALES;
PROC ARIMA;
IDENTIFY VAR=SALES(1);
ESTIMATE Q=1 NOCONSTANT PLOT;
FORECAST OUT=B1 BACK=0 LEAD=36;
TAB7-11.LIS
1 The SAS System
1
14:41 Monday, April 6,
1998
ARIMA Procedure
Name of variable = SALES.
Period(s) of Differencing = 1.
Mean of working series = 0.052424
Standard deviation = 1.313846
Number of observations = 99
NOTE: The first observation was eliminated by
differencing.
Autocorrelations
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 1.726190 1.00000 | |********************|
1 -0.602991 -0.34932 | *******| . |
2 -0.014746 -0.00854 | . | . |
3 0.0079905 0.00463 | . | . |
4 0.149170 0.08642 | . |** . |
5 -0.316581 -0.18340 | .****| . |
6 0.318011 0.18423 | . |****. |
7 -0.096487 -0.05590 | . *| . |
8 -0.040276 -0.02333 | . | . |
9 0.287988 0.16683 | . |*** . |
10 -0.186751 -0.10819 | . **| . |
11 0.108631 0.06293 | . |* . |
12 0.033949 0.01967 | . | . |
13 -0.081012 -0.04693 | . *| . |
14 0.082462 0.04777 | . |* . |
15 -0.028764 -0.01666 | . | . |
16 0.083399 0.04831 | . |* . |
17 0.078795 0.04565 | . |* . |
18 0.129775 0.07518 | . |** . |
19 -0.205131 -0.11883 | . **| . |
20 0.321816 0.18643 | . |****. |
21 -0.214211 -0.12409 | . **| . |
22 -0.0031001 -0.00180 | . | . |
23 0.143267 0.08300 | . |** . |
24 -0.160611 -0.09304 | . **| . |
"." marks two standard errors
1 The SAS System
2
14:41 Monday, April 6,
1998
ARIMA Procedure
Inverse Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 0.36477 | . |******* |
2 0.25258 | . |***** |
3 0.14517 | . |***. |
4 -0.01850 | . | . |
5 0.12033 | . |** . |
6 -0.09729 | . **| . |
7 -0.03350 | . *| . |
8 -0.05190 | . *| . |
9 -0.12722 | .***| . |
10 -0.01660 | . | . |
11 -0.07588 | . **| . |
12 -0.05237 | . *| . |
13 -0.06055 | . *| . |
14 -0.08527 | . **| . |
15 -0.12437 | . **| . |
16 -0.16155 | .***| . |
17 -0.15807 | .***| . |
18 -0.14523 | .***| . |
19 -0.04546 | . *| . |
20 -0.08854 | . **| . |
21 0.02834 | . |* . |
22 0.03306 | . |* . |
23 0.01826 | . | . |
24 0.08628 | . |** . |
1 The SAS System
3
14:41 Monday, April 6,
1998
ARIMA Procedure
Partial Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.34932 | *******| . |
2 -0.14871 | .***| . |
3 -0.05911 | . *| . |
4 0.07737 | . |** . |
5 -0.14208 | .***| . |
6 0.09208 | . |** . |
7 0.02320 | . | . |
8 -0.02057 | . | . |
9 0.20102 | . |**** |
10 -0.02794 | . *| . |
11 0.10093 | . |** . |
12 0.05634 | . |* . |
13 -0.04926 | . *| . |
14 0.10685 | . |** . |
15 -0.07045 | . *| . |
16 0.09031 | . |** . |
17 0.10260 | . |** . |
18 0.08986 | . |** . |
19 0.02422 | . | . |
20 0.12204 | . |** . |
21 -0.00634 | . | . |
22 -0.02735 | . *| . |
23 0.06334 | . |* . |
24 -0.11907 | . **| . |
Autocorrelation Check for White Noise
To Chi Autocorrelations
Lag Square DF Prob
6 20.47 6 0.002 -0.349 -0.009 0.005 0.086 -0.183 0.184
12 25.77 12 0.012 -0.056 -0.023 0.167 -0.108 0.063 0.020
18 27.56 18 0.069 -0.047 0.048 -0.017 0.048 0.046 0.075
24 37.76 24 0.037 -0.119 0.186 -0.124 -0.002 0.083 -0.093
1 The SAS System
4
14:41 Monday, April 6,
1998
ARIMA Procedure
Conditional Least Squares Estimation
Approx.
Parameter Estimate Std Error T Ratio Lag
MA1,1 0.39576 0.09296 4.26 1
Variance Estimate = 1.50355749
Std Error Estimate = 1.22619635
AIC = 322.320307*
SBC = 324.915427*
Number of Residuals= 99
* Does not include log determinant.
Autocorrelation Check of Residuals
To Chi Autocorrelations
Lag Square DF Prob
6 4.19 5 0.523 -0.007 -0.000 0.026 0.059 -0.107 0.154
12 8.56 11 0.662 0.010 0.039 0.174 -0.026 0.070 0.040
18 13.68 17 0.689 -0.012 0.057 0.039 0.106 0.121 0.107
24 18.38 23 0.736 -0.029 0.151 -0.074 -0.005 0.062 -0.060
Autocorrelation Plot of Residuals
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 1.503557 1.00000 | |********************|
1 -0.0098952 -0.00658 | . | . |
2 -0.0006982 -0.00046 | . | . |
3 0.038348 0.02550 | . |* . |
4 0.088988 0.05918 | . |* . |
5 -0.160171 -0.10653 | . **| . |
6 0.231047 0.15367 | . |***. |
7 0.015091 0.01004 | . | . |
8 0.058624 0.03899 | . |* . |
9 0.262155 0.17436 | . |***. |
10 -0.038681 -0.02573 | . *| . |
11 0.105135 0.06992 | . |* . |
12 0.060672 0.04035 | . |* . |
13 -0.018074 -0.01202 | . | . |
14 0.085044 0.05656 | . |* . |
15 0.058346 0.03881 | . |* . |
16 0.158908 0.10569 | . |** . |
17 0.181751 0.12088 | . |** . |
18 0.161567 0.10746 | . |** . |
19 -0.044115 -0.02934 | . *| . |
20 0.227708 0.15145 | . |***. |
21 -0.110844 -0.07372 | . *| . |
22 -0.0079882 -0.00531 | . | . |
23 0.092934 0.06181 | . |* . |
24 -0.090701 -0.06032 | . *| . |
"." marks two standard errors
1 The SAS System
5
14:41 Monday, April 6,
1998
ARIMA Procedure
Inverse Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.07250 | . *| . |
2 0.10272 | . |** . |
3 0.08634 | . |** . |
4 -0.14120 | .***| . |
5 0.20056 | . |**** |
6 -0.17522 | ****| . |
7 0.01971 | . | . |
8 -0.00280 | . | . |
9 -0.14832 | .***| . |
10 0.07719 | . |** . |
11 -0.07723 | . **| . |
12 -0.00310 | . | . |
13 -0.01716 | . | . |
14 -0.03843 | . *| . |
15 -0.04249 | . *| . |
16 -0.10634 | . **| . |
17 -0.07360 | . *| . |
18 -0.09986 | . **| . |
19 0.03054 | . |* . |
20 -0.09413 | . **| . |
21 0.05628 | . |* . |
22 0.02760 | . |* . |
23 -0.02411 | . | . |
24 0.10593 | . |** . |
1 The SAS System
6
14:41 Monday, April 6,
1998
ARIMA Procedure
Partial Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.00658 | . | . |
2 -0.00051 | . | . |
3 0.02550 | . |* . |
4 0.05956 | . |* . |
5 -0.10609 | . **| . |
6 0.15439 | . |***. |
7 0.00548 | . | . |
8 0.04312 | . |* . |
9 0.18612 | . |**** |
10 -0.06264 | . *| . |
11 0.11420 | . |** . |
12 0.00496 | . | . |
13 -0.02921 | . *| . |
14 0.10394 | . |** . |
15 -0.05293 | . *| . |
16 0.15582 | . |***. |
17 0.09247 | . |** . |
18 0.05971 | . |* . |
19 0.02355 | . | . |
20 0.08614 | . |** . |
21 -0.06206 | . *| . |
22 -0.01792 | . | . |
23 0.02293 | . | . |
24 -0.12683 | .***| . |
Model for variable SALES
No mean term in this model.
Period(s) of Differencing = 1.
Moving Average Factors
Factor 1: 1 - 0.39576 B**(1)
1 The SAS System
7
14:41 Monday, April 6,
1998
ARIMA Procedure
Forecasts for variable SALES
Obs Forecast Std Error Lower 95% Upper 95%
101 10.1734 1.2262 7.7701 12.5767
102 10.1734 1.4327 7.3654 12.9813
103 10.1734 1.6129 7.0121 13.3346
104 10.1734 1.7749 6.6946 13.6522
105 10.1734 1.9234 6.4036 13.9431
106 10.1734 2.0611 6.1336 14.2132
107 10.1734 2.1903 5.8805 14.4662
108 10.1734 2.3122 5.6416 14.7052
109 10.1734 2.4280 5.4146 14.9322
110 10.1734 2.5385 5.1980 15.1488
111 10.1734 2.6444 4.9904 15.3564
112 10.1734 2.7463 4.7908 15.5560
113 10.1734 2.8445 4.5983 15.7485
114 10.1734 2.9394 4.4123 15.9345
115 10.1734 3.0313 4.2321 16.1147
116 10.1734 3.1206 4.0572 16.2896
117 10.1734 3.2073 3.8872 16.4596
118 10.1734 3.2918 3.7216 16.6252
119 10.1734 3.3741 3.5602 16.7866
120 10.1734 3.4545 3.4027 16.9441
121 10.1734 3.5331 3.2487 17.0981
122 10.1734 3.6099 3.0980 17.2487
123 10.1734 3.6852 2.9506 17.3962
124 10.1734 3.7589 2.8060 17.5407
125 10.1734 3.8313 2.6643 17.6825
126 10.1734 3.9022 2.5251 17.8216
127 10.1734 3.9720 2.3885 17.9583
128 10.1734 4.0405 2.2542 18.0926
129 10.1734 4.1078 2.1222 18.2246
130 10.1734 4.1741 1.9923 18.3545
131 10.1734 4.2394 1.8644 18.4824
132 10.1734 4.3036 1.7384 18.6083
133 10.1734 4.3669 1.6143 18.7324
134 10.1734 4.4293 1.4920 18.8547
135 10.1734 4.4909 1.3714 18.9754
136 10.1734 4.5516 1.2524 19.0943
TAB7-12.SAS
options linesize=80;
data fad;
infile "fad.dat" obs=100;
input demand;
run;
proc arima;
identify var=demand(1) noprint;
estimate q=1 noconstant plot;
run;
run;
TAB7-12.LIS
1 The SAS System
1
13:05 Monday, February 16,
1998
ARIMA Procedure
Conditional Least Squares Estimation
Approx.
Parameter Estimate Std Error T Ratio Lag
MA1,1 0.39576 0.09296 4.26 1
Variance Estimate = 1.50355749
Std Error Estimate = 1.22619635
AIC = 322.320307*
SBC = 324.915427*
Number of Residuals= 99
* Does not include log determinant.
Autocorrelation Check of Residuals
To Chi Autocorrelations
Lag Square DF Prob
6 4.19 5 0.523 -0.007 -0.000 0.026 0.059 -0.107 0.154
12 8.56 11 0.662 0.010 0.039 0.174 -0.026 0.070 0.040
18 13.68 17 0.689 -0.012 0.057 0.039 0.106 0.121 0.107
24 18.38 23 0.736 -0.029 0.151 -0.074 -0.005 0.062 -0.060
Autocorrelation Plot of Residuals
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 1.503557 1.00000 | |********************|
1 -0.0098952 -0.00658 | . | . |
2 -0.0006982 -0.00046 | . | . |
3 0.038348 0.02550 | . |* . |
4 0.088988 0.05918 | . |* . |
5 -0.160171 -0.10653 | . **| . |
6 0.231047 0.15367 | . |***. |
7 0.015091 0.01004 | . | . |
8 0.058624 0.03899 | . |* . |
9 0.262155 0.17436 | . |***. |
10 -0.038681 -0.02573 | . *| . |
11 0.105135 0.06992 | . |* . |
12 0.060672 0.04035 | . |* . |
13 -0.018074 -0.01202 | . | . |
14 0.085044 0.05656 | . |* . |
15 0.058346 0.03881 | . |* . |
16 0.158908 0.10569 | . |** . |
17 0.181751 0.12088 | . |** . |
18 0.161567 0.10746 | . |** . |
19 -0.044115 -0.02934 | . *| . |
20 0.227708 0.15145 | . |***. |
21 -0.110844 -0.07372 | . *| . |
22 -0.0079882 -0.00531 | . | . |
23 0.092934 0.06181 | . |* . |
24 -0.090701 -0.06032 | . *| . |
"." marks two standard errors
1 The SAS System
2
13:05 Monday, February 16,
1998
ARIMA Procedure
Inverse Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.07250 | . *| . |
2 0.10272 | . |** . |
3 0.08634 | . |** . |
4 -0.14120 | .***| . |
5 0.20056 | . |**** |
6 -0.17522 | ****| . |
7 0.01971 | . | . |
8 -0.00280 | . | . |
9 -0.14832 | .***| . |
10 0.07719 | . |** . |
11 -0.07723 | . **| . |
12 -0.00310 | . | . |
13 -0.01716 | . | . |
14 -0.03843 | . *| . |
15 -0.04249 | . *| . |
16 -0.10634 | . **| . |
17 -0.07360 | . *| . |
18 -0.09986 | . **| . |
19 0.03054 | . |* . |
20 -0.09413 | . **| . |
21 0.05628 | . |* . |
22 0.02760 | . |* . |
23 -0.02411 | . | . |
24 0.10593 | . |** . |
1 The SAS System
3
13:05 Monday, February 16,
1998
ARIMA Procedure
Partial Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.00658 | . | . |
2 -0.00051 | . | . |
3 0.02550 | . |* . |
4 0.05956 | . |* . |
5 -0.10609 | . **| . |
6 0.15439 | . |***. |
7 0.00548 | . | . |
8 0.04312 | . |* . |
9 0.18612 | . |**** |
10 -0.06264 | . *| . |
11 0.11420 | . |** . |
12 0.00496 | . | . |
13 -0.02921 | . *| . |
14 0.10394 | . |** . |
15 -0.05293 | . *| . |
16 0.15582 | . |***. |
17 0.09247 | . |** . |
18 0.05971 | . |* . |
19 0.02355 | . | . |
20 0.08614 | . |** . |
21 -0.06206 | . *| . |
22 -0.01792 | . | . |
23 0.02293 | . | . |
24 -0.12683 | .***| . |
Model for variable DEMAND
No mean term in this model.
Period(s) of Differencing = 1.
Moving Average Factors
Factor 1: 1 - 0.39576 B**(1)
TAB7-13.SAS
options linesize=80;
data index;
infile "usind.dat" obs=271;
input date indx;
lagindx = lag(indx);
difindx = indx-lagindx;
lnindx = log(indx);
laglnind = lag(lnindx);
diflnind = lnindx-laglnind;
run;
proc arima;
identify var=lnindx(1) noprint;
estimate q=1 plot;
forecast out=fore lead=0;
run;
data convert;
set fore;
actual = exp(lnindx);
fitted = exp(forecast);
resid = actual - fitted;
er_ratio = resid/actual;
run;
*THE FOLLOWING TWO PROCEDURES GENERATE TABLE 7-16;
proc print data=convert;
var actual fitted resid er_ratio;
run;
proc means data=convert;
var actual fitted resid er_ratio;
run;
*THE FOLLOWING PROCEDURE GENERATES ALL BUT THE LAST LINE OF TABLE 7-13.;
*INFO CONTAINED IN THE LAST LINE OF TAB 7-13 CAN BE FOUND IN THE OUTPUT;
* OF THE ARIMA PROCEDURE ABOVE;
proc means data=index;
var indx difindx lnindx diflnind;
run;
run;
TAB7-13.LIS
1 The SAS System
1
22:45 Sunday, February 22,
1998
ARIMA Procedure
Conditional Least Squares Estimation
Approx.
Parameter Estimate Std Error T Ratio Lag
MU 0.0055954 0.0028806 1.94 0
MA1,1 -0.32357 0.05789 -5.59 1
Constant Estimate = 0.00559543
Variance Estimate = 0.00128177
Std Error Estimate = 0.03580185
AIC = -1029.8487*
SBC = -1022.6518*
Number of Residuals= 270
* Does not include log determinant.
Correlations of the Estimates
Parameter MU MA1,1
MU 1.000 -0.000
MA1,1 -0.000 1.000
Autocorrelation Check of Residuals
To Chi Autocorrelations
Lag Square DF Prob
6 1.27 5 0.938 -0.003 -0.010 -0.005 -0.008 0.046 -0.047
12 6.91 11 0.806 -0.096 0.015 -0.035 -0.032 0.084 -0.038
18 10.17 17 0.896 0.006 -0.043 -0.045 0.027 -0.073 0.035
24 16.73 23 0.822 -0.079 -0.072 -0.063 0.019 -0.080 -0.004
30 20.59 29 0.873 0.004 0.057 0.092 0.028 0.011 -0.015
36 25.40 35 0.883 -0.023 -0.077 0.006 0.074 0.037 -0.047
42 27.87 41 0.941 0.042 0.067 0.006 -0.031 -0.010 0.022
48 33.61 47 0.929 0.030 -0.088 -0.012 -0.004 0.064 -0.068
1 The SAS System
2
22:45 Sunday, February 22,
1998
ARIMA Procedure
Autocorrelation Plot of Residuals
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 0.0012818 1.00000 | |********************|
1 -4.443E-6 -0.00347 | . | . |
2 -0.0000126 -0.00982 | . | . |
3 -6.2247E-6 -0.00486 | . | . |
4 -9.7219E-6 -0.00758 | . | . |
5 0.00005918 0.04617 | . |*. |
6 -0.0000607 -0.04738 | .*| . |
7 -0.0001225 -0.09556 | **| . |
8 0.00001965 0.01533 | . | . |
9 -0.0000448 -0.03497 | .*| . |
10 -0.0000411 -0.03210 | .*| . |
11 0.0001073 0.08371 | . |** |
12 -0.0000486 -0.03793 | .*| . |
13 7.51882E-6 0.00587 | . | . |
14 -0.0000546 -0.04260 | .*| . |
15 -0.000058 -0.04527 | .*| . |
16 0.0000345 0.02691 | . |* . |
17 -0.000094 -0.07330 | . *| . |
18 0.00004545 0.03546 | . |* . |
19 -0.000101 -0.07882 | .**| . |
20 -0.0000929 -0.07249 | . *| . |
21 -0.0000811 -0.06329 | . *| . |
22 0.00002463 0.01921 | . | . |
23 -0.0001025 -0.07998 | .**| . |
24 -5.369E-6 -0.00419 | . | . |
"." marks two standard errors
1 The SAS System
3
22:45 Sunday, February 22,
1998
ARIMA Procedure
Inverse Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 0.01349 | . | . |
2 0.04513 | . |*. |
3 0.03844 | . |*. |
4 0.02745 | . |*. |
5 -0.02367 | . | . |
6 0.07287 | . |*. |
7 0.12637 | . |*** |
8 0.00185 | . | . |
9 0.04085 | . |*. |
10 0.05165 | . |*. |
11 -0.06143 | .*| . |
12 0.03183 | . |*. |
13 0.03641 | . |*. |
14 0.07038 | . |*. |
15 0.04472 | . |*. |
16 0.00798 | . | . |
17 0.08585 | . |** |
18 -0.04354 | .*| . |
19 0.08734 | . |** |
20 0.06904 | . |*. |
21 0.07839 | . |** |
22 -0.00350 | . | . |
23 0.08625 | . |** |
24 0.01784 | . | . |
1 The SAS System
4
22:45 Sunday, February 22,
1998
ARIMA Procedure
Partial Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.00347 | . | . |
2 -0.00983 | . | . |
3 -0.00493 | . | . |
4 -0.00772 | . | . |
5 0.04603 | . |*. |
6 -0.04735 | .*| . |
7 -0.09537 | **| . |
8 0.01434 | . | . |
9 -0.03657 | .*| . |
10 -0.03660 | .*| . |
11 0.08733 | . |** |
12 -0.03251 | .*| . |
13 -0.00481 | . | . |
14 -0.04707 | .*| . |
15 -0.04399 | .*| . |
16 0.00793 | . | . |
17 -0.07050 | .*| . |
18 0.04852 | . |*. |
19 -0.09037 | **| . |
20 -0.07037 | .*| . |
21 -0.07901 | **| . |
22 0.00569 | . | . |
23 -0.09233 | **| . |
24 -0.01913 | . | . |
Model for variable LNINDX
Estimated Mean = 0.00559543
Period(s) of Differencing = 1.
Moving Average Factors
Factor 1: 1 + 0.32357 B**(1)
1 The SAS System
5
22:45 Sunday, February 22,
1998
OBS ACTUAL FITTED RESID ER_RATIO
1 98.2 . . .
2 94.8 98.751 -3.9510 -0.04168
3 96.4 94.081 2.3193 0.02406
4 93.5 97.708 -4.2078 -0.04500
5 82.7 92.695 -9.9949 -0.12086
6 82.2 80.150 2.0502 0.02494
7 82.4 83.340 -0.9395 -0.01140
8 84.8 82.559 2.2411 0.02643
9 89.8 86.018 3.7819 0.04212
10 91.8 91.570 0.2301 0.00251
11 91.7 92.390 -0.6901 -0.00753
12 98.0 91.991 6.0089 0.06132
13 101.7 100.588 1.1116 0.01093
14 105.6 102.635 2.9650 0.02808
15 108.3 107.176 1.1244 0.01038
16 112.1 109.276 2.8239 0.02519
17 110.6 113.663 -3.0635 -0.02770
18 108.5 110.242 -1.7417 -0.01605
19 107.7 108.548 -0.8480 -0.00787
20 105.8 108.030 -2.2298 -0.02108
21 108.1 105.678 2.4219 0.02240
22 105.8 109.507 -3.7065 -0.03503
23 100.9 105.215 -4.3148 -0.04276
24 107.9 100.101 7.7994 0.07228
25 112.4 111.172 1.2282 0.01093
26 114.5 113.433 1.0668 0.00932
27 117.1 115.492 1.6083 0.01373
28 118.4 118.285 0.1148 0.00097
29 117.1 119.102 -2.0017 -0.01709
30 117.5 117.113 0.3870 0.00329
31 116.6 118.286 -1.6855 -0.01446
32 120.8 116.711 4.0890 0.03385
33 119.0 122.839 -3.8389 -0.03226
34 119.2 118.445 0.7554 0.00634
35 125.1 120.116 4.9843 0.03984
36 127.8 127.468 0.3321 0.00260
37 128.8 128.625 0.1747 0.00136
38 124.2 129.580 -5.3796 -0.04331
39 122.3 123.195 -0.8950 -0.00732
40 119.9 122.696 -2.7964 -0.02332
41 116.6 119.677 -3.0767 -0.02639
42 113.9 116.270 -2.3703 -0.02081
43 115.1 113.778 1.3217 0.01148
44 112.9 116.179 -3.2792 -0.02905
45 114.9 112.487 2.4134 0.02100
46 119.5 116.341 3.1589 0.02643
47 111.0 121.217 -10.2167 -0.09204
48 103.1 108.488 -5.3876 -0.05226
49 104.5 101.984 2.5162 0.02408
50 101.7 105.918 -4.2184 -0.04148
51 106.0 100.935 5.0654 0.04779
52 100.6 108.297 -7.6971 -0.07651
53 97.5 98.780 -1.2797 -0.01313
54 97.7 97.634 0.0657 0.00067
55 90.1 98.270 -8.1696 -0.09067
1 The SAS System
6
22:45 Sunday, February 22,
1998
OBS ACTUAL FITTED RESID ER_RATIO
56 82.7 88.096 -5.39640 -0.065253
57 74.1 81.480 -7.38033 -0.099600
58 75.5 72.261 3.23865 0.042896
59 78.0 77.008 0.99161 0.012713
60 73.0 78.763 -5.76306 -0.078946
61 78.9 71.627 7.27325 0.092183
62 87.1 81.865 5.23515 0.060105
63 91.1 89.363 1.73676 0.019064
64 92.2 92.184 0.01648 0.000179
65 98.0 92.723 5.27729 0.053850
66 100.5 100.331 0.16910 0.001683
67 100.6 101.119 -0.51900 -0.005159
68 93.2 100.996 -7.79618 -0.083650
69 92.1 91.318 0.78187 0.008489
70 96.3 92.873 3.42737 0.035591
71 98.0 97.983 0.01743 0.000178
72 96.5 98.556 -2.05556 -0.021301
73 105.4 96.382 9.01810 0.085561
74 109.5 109.104 0.39624 0.003619
75 110.0 110.244 -0.24366 -0.002215
76 110.9 110.538 0.36194 0.003264
77 110.0 111.640 -1.64030 -0.014912
78 110.7 110.089 0.61130 0.005522
79 113.3 111.521 1.77921 0.015704
80 112.4 114.521 -2.12076 -0.018868
81 114.7 112.349 2.35088 0.020496
82 110.8 116.119 -5.31907 -0.048006
83 110.1 109.744 0.35601 0.003234
84 113.8 110.834 2.96613 0.026064
85 112.9 115.421 -2.52066 -0.022327
86 109.8 112.725 -2.92522 -0.026641
87 109.4 109.481 -0.08072 -0.000738
88 107.7 109.988 -2.28760 -0.021241
89 107.4 107.570 -0.17026 -0.001585
90 108.0 107.947 0.05271 0.000488
91 109.0 108.623 0.37684 0.003457
92 106.3 109.735 -3.43451 -0.032310
93 104.7 105.802 -1.10224 -0.010528
94 102.0 104.931 -2.93131 -0.028738
95 102.6 101.636 0.96372 0.009393
96 102.1 103.491 -1.39124 -0.013626
97 98.2 102.224 -4.02425 -0.040980
98 96.8 97.476 -0.67601 -0.006984
99 96.6 97.124 -0.52420 -0.005427
100 100.8 96.972 3.82792 0.037975
101 106.0 102.643 3.35660 0.031666
102 106.2 107.710 -1.51043 -0.014222
103 105.7 106.309 -0.60901 -0.005762
104 113.0 106.096 6.90431 0.061100
105 113.0 115.976 -2.97597 -0.026336
106 109.4 112.682 -3.28226 -0.030002
107 103.3 108.967 -5.66659 -0.054856
108 104.5 102.100 2.39997 0.022966
109 108.5 105.879 2.62064 0.024153
110 106.9 109.975 -3.07541 -0.028769
1 The SAS System
7
22:45 Sunday, February 22,
1998
OBS ACTUAL FITTED RESID ER_RATIO
111 108.9 106.518 2.3822 0.02188
112 111.0 110.298 0.7024 0.00633
113 108.5 111.852 -3.3523 -0.03090
114 110.7 108.040 2.6602 0.02403
115 111.7 112.201 -0.5008 -0.00448
116 116.8 112.164 4.6357 0.03969
117 118.1 119.005 -0.9046 -0.00766
118 113.6 118.470 -4.8698 -0.04287
119 112.8 112.696 0.1036 0.00092
120 117.2 113.467 3.7333 0.03185
121 120.6 119.099 1.5014 0.01245
122 125.5 121.769 3.7307 0.02973
123 113.9 127.443 -13.5426 -0.11890
124 112.0 110.450 1.5498 0.01384
125 117.1 113.137 3.9626 0.03384
126 124.6 119.076 5.5239 0.04433
127 130.4 127.151 3.2489 0.02491
128 134.3 132.207 2.0934 0.01559
129 137.6 135.742 1.8582 0.01350
130 141.7 138.982 2.7178 0.01918
131 147.6 143.391 4.2092 0.02852
132 145.2 149.824 -4.6242 -0.03185
133 144.6 144.541 0.0590 0.00041
134 139.7 145.431 -5.7306 -0.04102
135 144.9 138.668 6.2317 0.04301
136 146.2 147.800 -1.6004 -0.01095
137 143.3 146.503 -3.2033 -0.02235
138 143.9 143.077 0.8231 0.00572
139 140.5 144.976 -4.4763 -0.03186
140 141.0 139.862 1.1382 0.00807
141 128.7 142.164 -13.4635 -0.10461
142 130.3 125.322 4.9780 0.03820
143 133.7 132.693 1.0069 0.00753
144 134.7 134.779 -0.0795 -0.00059
145 127.6 135.430 -7.8300 -0.06136
146 124.6 125.867 -1.2670 -0.01017
147 120.6 124.890 -4.2896 -0.03557
148 126.5 119.913 6.5871 0.05207
149 126.6 129.430 -2.8301 -0.02235
150 119.7 126.403 -6.7029 -0.05600
151 119.0 118.268 0.7319 0.00615
152 119.3 119.907 -0.6068 -0.00509
153 133.2 119.773 13.4274 0.10081
154 144.3 138.633 5.6672 0.03927
155 150.2 147.003 3.1969 0.02128
156 151.6 152.098 -0.4979 -0.00328
157 156.9 152.289 4.6110 0.02939
158 159.7 159.311 0.3894 0.00244
159 165.2 160.723 4.4770 0.02710
160 171.6 167.610 3.9896 0.02325
161 178.5 173.881 4.6186 0.02587
162 181.0 181.031 -0.0307 -0.00017
163 181.6 182.006 -0.4056 -0.00223
164 176.7 182.487 -5.7872 -0.03275
165 181.8 175.848 5.9518 0.03274
1 The SAS System
8
22:45 Sunday, February 22,
1998
OBS ACTUAL FITTED RESID ER_RATIO
166 182.4 184.800 -2.3998 -0.01316
167 179.7 182.649 -2.9494 -0.01641
168 178.8 179.759 -0.9589 -0.00536
169 181.0 179.492 1.5077 0.00833
170 171.1 182.509 -11.4089 -0.06668
171 171.3 168.504 2.7964 0.01632
172 171.4 173.181 -1.7810 -0.01039
173 170.3 171.786 -1.4862 -0.00873
174 166.6 170.775 -4.1748 -0.02506
175 164.3 166.199 -1.8985 -0.01156
176 178.9 164.609 14.2912 0.07988
177 180.7 184.816 -4.1161 -0.02278
178 179.3 180.394 -1.0945 -0.00610
179 180.9 179.951 0.9486 0.00524
180 178.9 182.225 -3.3248 -0.01858
181 186.7 178.835 7.8649 0.04213
182 196.8 190.380 6.4195 0.03262
183 195.2 200.039 -4.8393 -0.02479
184 196.5 194.746 1.7540 0.00893
185 201.1 198.177 2.9233 0.01454
186 205.5 203.189 2.3112 0.01125
187 209.4 207.411 1.9893 0.00950
188 204.8 211.226 -6.4263 -0.03138
189 200.2 203.901 -3.7005 -0.01848
190 202.5 200.134 2.3662 0.01169
191 214.8 204.412 10.3878 0.04836
192 225.5 219.498 6.0023 0.02662
193 226.5 228.753 -2.2535 -0.00995
194 238.6 227.042 11.5575 0.04844
195 252.7 243.825 8.8753 0.03512
196 258.9 257.075 1.8252 0.00705
197 259.4 260.949 -1.5494 -0.00597
198 266.8 260.353 6.4466 0.02416
199 261.3 270.429 -9.1289 -0.03494
200 266.5 259.863 6.6373 0.02491
201 259.2 270.191 -10.9913 -0.04240
202 258.2 257.175 1.0248 0.00397
203 266.6 259.983 6.6169 0.02482
204 270.4 270.285 0.1150 0.00043
205 287.7 271.955 15.7453 0.05473
206 305.6 294.631 10.9686 0.03589
207 318.1 310.971 7.1290 0.02241
208 314.7 322.240 -7.5396 -0.02396
209 314.5 314.051 0.4492 0.00143
210 327.8 316.411 11.3890 0.03474
211 337.3 333.433 3.8673 0.01147
212 358.3 340.461 17.8394 0.04979
213 346.6 366.314 -19.7141 -0.05688
214 304.8 342.361 -37.5615 -0.12323
215 266.5 295.199 -28.6988 -0.10769
216 262.1 259.272 2.8282 0.01079
217 272.5 264.498 8.0024 0.02937
218 280.8 276.685 4.1153 0.01466
219 289.1 283.728 5.3722 0.01858
220 285.7 292.492 -6.7920 -0.02377
1 The SAS System
9
22:45 Sunday, February 22,
1998
OBS ACTUAL FITTED RESID ER_RATIO
221 278.6 285.127 -6.5272 -0.02343
222 294.4 278.072 16.3283 0.05546
223 292.7 301.569 -8.8686 -0.03030
224 286.9 291.513 -4.6132 -0.01608
225 291.5 287.025 4.4755 0.01535
226 301.8 294.607 7.1931 0.02383
227 294.8 305.872 -11.0716 -0.03756
228 300.8 292.939 7.8613 0.02613
229 310.5 305.091 5.4091 0.01742
230 319.8 314.023 5.7772 0.01806
231 318.4 323.497 -5.0970 -0.01601
232 328.9 318.545 10.3546 0.03148
233 341.5 334.187 7.3134 0.02142
234 352.2 345.830 6.3699 0.01809
235 361.1 356.274 4.8260 0.01336
236 377.0 364.710 12.2895 0.03260
237 377.8 383.203 -5.4027 -0.01430
238 377.9 378.178 -0.2784 -0.00074
239 370.1 379.930 -9.8299 -0.02656
240 379.2 369.033 10.1667 0.02681
241 369.8 384.696 -14.8958 -0.04028
242 359.5 367.153 -7.6535 -0.02129
243 368.2 359.061 9.1386 0.02482
244 367.9 373.289 -5.3894 -0.01465
245 381.0 368.228 12.7725 0.03352
246 392.0 387.388 4.6116 0.01176
247 391.6 395.712 -4.1119 -0.01050
248 359.8 392.469 -32.6686 -0.09080
249 343.1 351.786 -8.6860 -0.02532
250 334.1 342.245 -8.1453 -0.02438
251 343.0 333.366 9.6337 0.02809
252 357.6 348.119 9.4812 0.02651
253 354.1 362.747 -8.6468 -0.02442
254 394.1 353.318 40.7820 0.10348
255 405.0 410.570 -5.5696 -0.01375
256 413.0 405.477 7.5234 0.01822
257 411.2 417.795 -6.5953 -0.01604
258 411.5 411.384 0.1162 0.00028
259 413.6 413.847 -0.2468 -0.00060
260 423.6 415.840 7.7595 0.01832
261 421.2 428.533 -7.3327 -0.01741
262 420.8 421.205 -0.4046 -0.00096
263 419.8 423.030 -3.2296 -0.00769
264 422.6 421.110 1.4900 0.00353
265 452.6 425.457 27.1428 0.05997
266 448.8 464.339 -15.5391 -0.03462
267 443.1 446.375 -3.2749 -0.00739
268 443.2 444.526 -1.3259 -0.00299
269 451.2 445.256 5.9437 0.01317
270 444.1 455.683 -11.5828 -0.02608
271 451.5 442.887 8.6132 0.01908
1 The SAS System
10
22:45 Sunday, February 22,
1998
Variable N Mean Std Dev Minimum Maximum
---------------------------------------------------------------------
ACTUAL 271 188.0188192 107.2613249 73.0000000 452.6000000
FITTED 270 188.1843266 107.0411157 71.6267535 464.3390564
RESID 270 0.1671548 7.3016362 -37.5614793 40.7820133
ER_RATIO 270 -0.000580407 0.0360271 -0.1232332 0.1034814
---------------------------------------------------------------------
1 The SAS System
11
22:45 Sunday, February 22,
1998
Variable N Mean Std Dev Minimum Maximum
---------------------------------------------------------------------
INDX 271 188.0188192 107.2613249 73.0000000 452.6000000
DIFINDX 270 1.3085185 7.7179630 -41.8000000 40.0000000
LNINDX 271 5.0950604 0.5151021 4.2904594 6.1150087
DIFLNIND 270 0.0056503 0.0375192 -0.1342816 0.1102104
---------------------------------------------------------------------
TAB7-14.SAS
options linesize=80;
data index;
infile "usind.dat" obs=271;
input date indx;
lagindx = lag(indx);
difindx = indx-lagindx;
lnindx = log(indx);
laglnind = lag(lnindx);
diflnind = lnindx-laglnind;
run;
proc arima;
identify var=lnindx(1) noprint;
estimate q=1 plot;
forecast out=fore lead=0;
run;
data convert;
set fore;
actual = exp(lnindx);
fitted = exp(forecast);
resid = actual - fitted;
er_ratio = resid/actual;
run;
*THE FOLLOWING TWO PROCEDURES GENERATE TABLE 7-16;
proc print data=convert;
var actual fitted resid er_ratio;
run;
proc means data=convert;
var actual fitted resid er_ratio;
run;
*THE FOLLOWING PROCEDURE GENERATES ALL BUT THE LAST LINE OF TABLE 7-13.;
*INFO CONTAINED IN THE LAST LINE OF TAB 7-13 CAN BE FOUND IN THE OUTPUT;
* OF THE ARIMA PROCEDURE ABOVE;
proc means data=index;
var indx difindx lnindx diflnind;
run;
run;
TAB7-14.LIS
1 The SAS System
1
13:43 Monday, February 16,
1998
ARIMA Procedure
Variance Estimate = 0.00143441
Std Error Estimate = 0.03787354
AIC = -1001.4645*
SBC = -1001.4645*
Number of Residuals= 270
* Does not include log determinant.
Autocorrelation Check of Residuals
To Chi Autocorrelations
Lag Square DF Prob
6 26.59 6 0.000 0.303 0.011 0.013 0.029 0.055 -0.035
12 30.50 12 0.002 -0.080 0.001 -0.016 0.006 0.084 0.010
18 31.44 18 0.026 0.004 -0.032 -0.028 0.012 -0.034 0.008
24 37.29 24 0.041 -0.068 -0.094 -0.059 -0.002 -0.054 -0.004
30 48.27 30 0.019 0.039 0.102 0.133 0.076 0.033 0.001
36 54.46 36 0.025 -0.029 -0.061 0.025 0.104 0.063 -0.006
42 59.82 42 0.036 0.065 0.097 0.033 -0.014 0.007 0.045
48 63.02 48 0.072 0.028 -0.064 -0.021 0.028 0.061 0.003
1 The SAS System
2
13:43 Monday, February 16,
1998
ARIMA Procedure
Autocorrelation Plot of Residuals
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 0.0014344 1.00000 | |********************|
1 0.00043493 0.30321 | . |****** |
2 0.00001579 0.01101 | . | . |
3 0.00001863 0.01299 | . | . |
4 0.00004203 0.02930 | . |* . |
5 0.00007875 0.05490 | . |* . |
6 -0.0000503 -0.03506 | . *| . |
7 -0.0001145 -0.07986 | .**| . |
8 9.85274E-7 0.00069 | . | . |
9 -0.000023 -0.01601 | . | . |
10 8.15902E-6 0.00569 | . | . |
11 0.00012101 0.08436 | . |**. |
12 0.00001392 0.00970 | . | . |
13 5.10577E-6 0.00356 | . | . |
14 -0.0000464 -0.03235 | . *| . |
15 -0.0000408 -0.02843 | . *| . |
16 0.00001775 0.01237 | . | . |
17 -0.0000488 -0.03405 | . *| . |
18 0.00001193 0.00832 | . | . |
19 -0.0000979 -0.06826 | . *| . |
20 -0.0001347 -0.09388 | .**| . |
21 -0.0000848 -0.05911 | . *| . |
22 -3.0104E-6 -0.00210 | . | . |
23 -0.0000771 -0.05373 | . *| . |
24 -5.9731E-6 -0.00416 | . | . |
"." marks two standard errors
1 The SAS System
3
13:43 Monday, February 16,
1998
ARIMA Procedure
Inverse Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.35363 | *******| . |
2 0.11573 | . |** |
3 -0.04253 | .*| . |
4 0.01782 | . | . |
5 -0.06684 | .*| . |
6 0.02577 | . |*. |
7 0.08472 | . |** |
8 -0.05557 | .*| . |
9 0.01017 | . | . |
10 0.03996 | . |*. |
11 -0.09869 | **| . |
12 0.03413 | . |*. |
13 -0.01212 | . | . |
14 0.03330 | . |*. |
15 0.01357 | . | . |
16 -0.04809 | .*| . |
17 0.09024 | . |** |
18 -0.10972 | **| . |
19 0.08513 | . |** |
20 -0.00586 | . | . |
21 0.06654 | . |*. |
22 -0.06974 | .*| . |
23 0.08418 | . |** |
24 -0.03868 | .*| . |
1 The SAS System
4
13:43 Monday, February 16,
1998
ARIMA Procedure
Partial Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 0.30321 | . |****** |
2 -0.08912 | **| . |
3 0.04038 | . |*. |
4 0.01540 | . | . |
5 0.04603 | . |*. |
6 -0.07221 | .*| . |
7 -0.04760 | .*| . |
8 0.04019 | . |*. |
9 -0.03936 | .*| . |
10 0.02733 | . |*. |
11 0.08916 | . |** |
12 -0.04379 | .*| . |
13 0.01351 | . | . |
14 -0.04570 | .*| . |
15 -0.00578 | . | . |
16 0.00820 | . | . |
17 -0.03559 | .*| . |
18 0.05062 | . |*. |
19 -0.10470 | **| . |
20 -0.03700 | .*| . |
21 -0.03540 | .*| . |
22 0.02046 | . | . |
23 -0.06914 | .*| . |
24 0.04653 | . |*. |
Model for variable LNINDEX
No mean term in this model.
Period(s) of Differencing = 1.
TAB7-15.SAS
OPTION LINESIZE=80;
DATA USIND;
INFILE USIND;
INPUT DATE WHY;
LWHY = LOG(WHY);
PROC ARIMA;
IDENTIFY VAR=LWHY(1);
ESTIMATE Q=1 PLOT;
IDENTIFY VAR=LWHY;
ESTIMATE P=1 Q=1;
FORECAST OUT=B1 BACK=0 LEAD=36;
TAB7-15.LIS
1 The SAS System
1
14:41 Monday, April 6,
1998
ARIMA Procedure
Name of variable = LWHY.
Period(s) of Differencing = 1.
Mean of working series = 0.00565
Standard deviation = 0.03745
Number of observations = 270
NOTE: The first observation was eliminated by
differencing.
Autocorrelations
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 0.0014025 1.00000 | |********************|
1 0.00040249 0.28699 | . |****** |
2 -0.0000167 -0.01194 | . | . |
3 -0.0000143 -0.01019 | . | . |
4 6.42764E-6 0.00458 | . | . |
5 0.00004264 0.03040 | . |* . |
6 -0.0000867 -0.06178 | . *| . |
7 -0.000149 -0.10623 | .**| . |
8 -0.0000322 -0.02298 | . | . |
9 -0.0000559 -0.03985 | . *| . |
10 -0.0000249 -0.01777 | . | . |
11 0.00008907 0.06351 | . |* . |
12 -0.0000169 -0.01202 | . | . |
13 -0.0000249 -0.01775 | . | . |
14 -0.000076 -0.05418 | . *| . |
15 -0.0000699 -0.04980 | . *| . |
16 -0.0000113 -0.00806 | . | . |
17 -0.0000778 -0.05550 | . *| . |
18 -0.0000151 -0.01077 | . | . |
19 -0.0001257 -0.08959 | .**| . |
20 -0.0001612 -0.11494 | .**| . |
21 -0.0001113 -0.07939 | .**| . |
22 -0.0000312 -0.02226 | . | . |
23 -0.000105 -0.07486 | . *| . |
24 -0.0000349 -0.02491 | . | . |
"." marks two standard errors
1 The SAS System
2
14:41 Monday, April 6,
1998
ARIMA Procedure
Inverse Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.32116 | ******| . |
2 0.13434 | . |*** |
3 -0.01899 | . | . |
4 0.03906 | . |*. |
5 -0.04383 | .*| . |
6 0.04114 | . |*. |
7 0.10266 | . |** |
8 -0.03751 | .*| . |
9 0.02693 | . |*. |
10 0.05743 | . |*. |
11 -0.08192 | **| . |
12 0.04933 | . |*. |
13 0.00081 | . | . |
14 0.04898 | . |*. |
15 0.03023 | . |*. |
16 -0.03309 | .*| . |
17 0.10603 | . |** |
18 -0.09407 | **| . |
19 0.09512 | . |** |
20 0.00692 | . | . |
21 0.07671 | . |** |
22 -0.05212 | .*| . |
23 0.08940 | . |** |
24 -0.01440 | . | . |
1 The SAS System
3
14:41 Monday, April 6,
1998
ARIMA Procedure
Partial Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 0.28699 | . |****** |
2 -0.10276 | **| . |
3 0.02542 | . |*. |
4 -0.00086 | . | . |
5 0.03126 | . |*. |
6 -0.08801 | **| . |
7 -0.06371 | .*| . |
8 0.02351 | . | . |
9 -0.05594 | .*| . |
10 0.00972 | . | . |
11 0.07405 | . |*. |
12 -0.05813 | .*| . |
13 -0.00134 | . | . |
14 -0.06087 | .*| . |
15 -0.02155 | . | . |
16 -0.00831 | . | . |
17 -0.05252 | .*| . |
18 0.03478 | . |*. |
19 -0.12323 | **| . |
20 -0.05720 | .*| . |
21 -0.05883 | .*| . |
22 -0.00471 | . | . |
23 -0.09598 | **| . |
24 0.01722 | . | . |
Autocorrelation Check for White Noise
To Chi Autocorrelations
Lag Square DF Prob
6 23.88 6 0.001 0.287 -0.012 -0.010 0.005 0.030 -0.062
12 28.90 12 0.004 -0.106 -0.023 -0.040 -0.018 0.064 -0.012
18 31.49 18 0.025 -0.018 -0.054 -0.050 -0.008 -0.056 -0.011
24 41.58 24 0.014 -0.090 -0.115 -0.079 -0.022 -0.075 -0.025
1 The SAS System
4
14:41 Monday, April 6,
1998
ARIMA Procedure
Conditional Least Squares Estimation
Approx.
Parameter Estimate Std Error T Ratio Lag
MU 0.0055954 0.0028806 1.94 0
MA1,1 -0.32357 0.05789 -5.59 1
Constant Estimate = 0.00559543
Variance Estimate = 0.00128177
Std Error Estimate = 0.03580185
AIC = -1029.8487*
SBC = -1022.6518*
Number of Residuals= 270
* Does not include log determinant.
Correlations of the Estimates
Parameter MU MA1,1
MU 1.000 -0.000
MA1,1 -0.000 1.000
Autocorrelation Check of Residuals
To Chi Autocorrelations
Lag Square DF Prob
6 1.27 5 0.938 -0.003 -0.010 -0.005 -0.008 0.046 -0.047
12 6.91 11 0.806 -0.096 0.015 -0.035 -0.032 0.084 -0.038
18 10.17 17 0.896 0.006 -0.043 -0.045 0.027 -0.073 0.035
24 16.73 23 0.822 -0.079 -0.072 -0.063 0.019 -0.080 -0.004
30 20.59 29 0.873 0.004 0.057 0.092 0.028 0.011 -0.015
36 25.40 35 0.883 -0.023 -0.077 0.006 0.074 0.037 -0.047
42 27.87 41 0.941 0.042 0.067 0.006 -0.031 -0.010 0.022
48 33.61 47 0.929 0.030 -0.088 -0.012 -0.004 0.064 -0.068
1 The SAS System
5
14:41 Monday, April 6,
1998
ARIMA Procedure
Autocorrelation Plot of Residuals
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 0.0012818 1.00000 | |********************|
1 -4.443E-6 -0.00347 | . | . |
2 -0.0000126 -0.00982 | . | . |
3 -6.2247E-6 -0.00486 | . | . |
4 -9.7219E-6 -0.00758 | . | . |
5 0.00005918 0.04617 | . |*. |
6 -0.0000607 -0.04738 | .*| . |
7 -0.0001225 -0.09556 | **| . |
8 0.00001965 0.01533 | . | . |
9 -0.0000448 -0.03497 | .*| . |
10 -0.0000411 -0.03210 | .*| . |
11 0.0001073 0.08371 | . |** |
12 -0.0000486 -0.03793 | .*| . |
13 7.51882E-6 0.00587 | . | . |
14 -0.0000546 -0.04260 | .*| . |
15 -0.000058 -0.04527 | .*| . |
16 0.0000345 0.02691 | . |* . |
17 -0.000094 -0.07330 | . *| . |
18 0.00004545 0.03546 | . |* . |
19 -0.000101 -0.07882 | .**| . |
20 -0.0000929 -0.07249 | . *| . |
21 -0.0000811 -0.06329 | . *| . |
22 0.00002463 0.01921 | . | . |
23 -0.0001025 -0.07998 | .**| . |
24 -5.369E-6 -0.00419 | . | . |
"." marks two standard errors
1 The SAS System
6
14:41 Monday, April 6,
1998
ARIMA Procedure
Inverse Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 0.01349 | . | . |
2 0.04513 | . |*. |
3 0.03844 | . |*. |
4 0.02745 | . |*. |
5 -0.02367 | . | . |
6 0.07287 | . |*. |
7 0.12637 | . |*** |
8 0.00185 | . | . |
9 0.04085 | . |*. |
10 0.05165 | . |*. |
11 -0.06143 | .*| . |
12 0.03183 | . |*. |
13 0.03641 | . |*. |
14 0.07038 | . |*. |
15 0.04472 | . |*. |
16 0.00798 | . | . |
17 0.08585 | . |** |
18 -0.04354 | .*| . |
19 0.08734 | . |** |
20 0.06904 | . |*. |
21 0.07839 | . |** |
22 -0.00350 | . | . |
23 0.08625 | . |** |
24 0.01784 | . | . |
1 The SAS System
7
14:41 Monday, April 6,
1998
ARIMA Procedure
Partial Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.00347 | . | . |
2 -0.00983 | . | . |
3 -0.00493 | . | . |
4 -0.00772 | . | . |
5 0.04603 | . |*. |
6 -0.04735 | .*| . |
7 -0.09537 | **| . |
8 0.01434 | . | . |
9 -0.03657 | .*| . |
10 -0.03660 | .*| . |
11 0.08733 | . |** |
12 -0.03251 | .*| . |
13 -0.00481 | . | . |
14 -0.04707 | .*| . |
15 -0.04399 | .*| . |
16 0.00793 | . | . |
17 -0.07050 | .*| . |
18 0.04852 | . |*. |
19 -0.09037 | **| . |
20 -0.07037 | .*| . |
21 -0.07901 | **| . |
22 0.00569 | . | . |
23 -0.09233 | **| . |
24 -0.01913 | . | . |
Model for variable LWHY
Estimated Mean = 0.00559543
Period(s) of Differencing = 1.
Moving Average Factors
Factor 1: 1 + 0.32357 B**(1)
1 The SAS System
8
14:41 Monday, April 6,
1998
ARIMA Procedure
Name of variable = LWHY.
Mean of working series = 5.09506
Standard deviation = 0.514151
Number of observations = 271
Autocorrelations
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 0.264351 1.00000 | |********************|
1 0.261250 0.98827 | . |********************|
2 0.257712 0.97488 | . |******************* |
3 0.254129 0.96133 | . |******************* |
4 0.250539 0.94775 | . |******************* |
5 0.246677 0.93314 | . |******************* |
6 0.242677 0.91801 | . |****************** |
7 0.238700 0.90297 | . |****************** |
8 0.235148 0.88953 | . |****************** |
9 0.231728 0.87659 | . |****************** |
10 0.228364 0.86386 | . |***************** |
11 0.224985 0.85108 | . |***************** |
12 0.221589 0.83824 | . |***************** |
13 0.218339 0.82594 | . |***************** |
14 0.215173 0.81397 | . |**************** |
15 0.212103 0.80235 | . |**************** |
16 0.209122 0.79108 | . |**************** |
17 0.206172 0.77992 | . |**************** |
18 0.203337 0.76919 | . |*************** |
19 0.200878 0.75989 | . |*************** |
20 0.198446 0.75069 | . |*************** |
21 0.196346 0.74275 | . |*************** |
22 0.194388 0.73534 | . |*************** |
23 0.192244 0.72723 | . |*************** |
24 0.190125 0.71921 | . |************** |
"." marks two standard errors
1 The SAS System
9
14:41 Monday, April 6,
1998
ARIMA Procedure
Inverse Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.52928 | ***********| . |
2 0.02633 | . |*. |
3 0.02614 | . |*. |
4 -0.03848 | .*| . |
5 0.00750 | . | . |
6 -0.02182 | . | . |
7 0.05486 | . |*. |
8 -0.02237 | . | . |
9 0.00195 | . | . |
10 -0.00472 | . | . |
11 -0.01092 | . | . |
12 0.01467 | . | . |
13 -0.00485 | . | . |
14 0.00327 | . | . |
15 0.00390 | . | . |
16 -0.01218 | . | . |
17 -0.01784 | . | . |
18 0.05651 | . |*. |
19 -0.06166 | .*| . |
20 0.04283 | . |*. |
21 0.01387 | . | . |
22 -0.04801 | .*| . |
23 0.02123 | . | . |
24 -0.00090 | . | . |
1 The SAS System
10
14:41 Monday, April 6,
1998
ARIMA Procedure
Partial Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 0.98827 | . |********************|
2 -0.07683 | **| . |
3 -0.00897 | . | . |
4 -0.00767 | . | . |
5 -0.05105 | .*| . |
6 -0.02398 | . | . |
7 -0.00110 | . | . |
8 0.06108 | . |*. |
9 0.00675 | . | . |
10 0.00078 | . | . |
11 -0.01037 | . | . |
12 -0.01557 | . | . |
13 0.01341 | . | . |
14 0.00315 | . | . |
15 0.01202 | . | . |
16 0.00862 | . | . |
17 -0.00385 | . | . |
18 0.00985 | . | . |
19 0.05047 | . |*. |
20 -0.00842 | . | . |
21 0.04967 | . |*. |
22 0.01264 | . | . |
23 -0.04174 | .*| . |
24 0.00194 | . | . |
Autocorrelation Check for White Noise
To Chi Autocorrelations
Lag Square DF Prob
6 1510.48 6 0.000 0.988 0.975 0.961 0.948 0.933 0.918
12 2796.90 12 0.000 0.903 0.890 0.877 0.864 0.851 0.838
18 3901.04 18 0.000 0.826 0.814 0.802 0.791 0.780 0.769
24 4873.29 24 0.000 0.760 0.751 0.743 0.735 0.727 0.719
1 The SAS System
11
14:41 Monday, April 6,
1998
ARIMA Procedure
WARNING: The model defined by the new estimates is unstable. The iteration
process has been terminated.
WARNING: Estimates may not have converged.
ARIMA Estimation Optimization Summary
Estimation Method: Conditional Least Squares
Parameters Estimated: 3
Termination Criteria: Maximum Relative Change in Estimates
Iteration Stopping Value: 0.001
Criteria Value: 0.17847517
Maximum Absolute Value of Gradient: 0.51976609
R-Square (Relative Change in Regression SSE) from Last Iteration
Step: 0.11278341
Objective Function: Sum of Squared Residuals
Objective Function Value: 0.34961202
Marquardt's Lambda Coefficient: 1E-6
Numerical Derivative Perturbation Delta: 0.001
Iterations: 11
Warning Message: Estimates may not have converged.
Conditional Least Squares Estimation
Approx.
Parameter Estimate Std Error T Ratio Lag
MU 4.61314 0.03470 132.94 0
MA1,1 -0.27744 0.06025 -4.60 1
AR1,1 1.00000 0.0040310 248.08 1
Constant Estimate = 1.04805E-7
Variance Estimate = 0.00130452
Std Error Estimate = 0.03611817
AIC = -1027.9119*
SBC = -1017.1055*
Number of Residuals= 271
* Does not include log determinant.
Correlations of the Estimates
Parameter MU MA1,1 AR1,1
MU 1.000 0.008 0.001
MA1,1 0.008 1.000 0.119
AR1,1 0.001 0.119 1.000
1 The SAS System
12
14:41 Monday, April 6,
1998
ARIMA Procedure
Autocorrelation Check of Residuals
To Chi Autocorrelations
Lag Square DF Prob
6 2.39 4 0.665 0.059 -0.009 0.013 0.020 0.059 -0.031
12 6.95 10 0.730 -0.081 0.023 -0.021 -0.012 0.090 -0.019
18 9.26 16 0.902 0.014 -0.030 -0.033 0.036 -0.053 0.040
24 14.25 22 0.892 -0.062 -0.069 -0.049 0.031 -0.070 0.004
30 20.10 28 0.861 0.020 0.072 0.106 0.046 0.022 0.000
36 24.90 34 0.872 -0.017 -0.062 0.019 0.086 0.049 -0.034
42 28.66 40 0.909 0.058 0.081 0.020 -0.018 0.004 0.035
48 33.90 46 0.907 0.041 -0.074 -0.010 0.018 0.076 -0.050
Model for variable LWHY
Estimated Mean = 4.61314159
Autoregressive Factors
Factor 1: 1 - 1 B**(1)
Moving Average Factors
Factor 1: 1 + 0.27744 B**(1)
1 The SAS System
13
14:41 Monday, April 6,
1998
ARIMA Procedure
Forecasts for variable LWHY
Obs Forecast Std Error Lower 95% Upper 95%
272 6.1188 0.0361 6.0480 6.1895
273 6.1188 0.0586 6.0039 6.2336
274 6.1188 0.0746 5.9726 6.2649
275 6.1188 0.0877 5.9469 6.2906
276 6.1188 0.0991 5.9245 6.3130
277 6.1188 0.1093 5.9045 6.3330
278 6.1188 0.1186 5.8862 6.3513
279 6.1188 0.1273 5.8692 6.3683
280 6.1188 0.1354 5.8534 6.3841
281 6.1188 0.1431 5.8384 6.3991
282 6.1188 0.1503 5.8242 6.4133
283 6.1188 0.1572 5.8106 6.4269
284 6.1188 0.1639 5.7976 6.4399
285 6.1188 0.1702 5.7851 6.4524
286 6.1188 0.1764 5.7731 6.4644
287 6.1188 0.1823 5.7614 6.4761
288 6.1188 0.1881 5.7502 6.4873
289 6.1188 0.1936 5.7392 6.4983
290 6.1188 0.1991 5.7286 6.5089
291 6.1188 0.2043 5.7183 6.5192
292 6.1188 0.2095 5.7082 6.5293
293 6.1188 0.2145 5.6983 6.5392
294 6.1188 0.2194 5.6887 6.5488
295 6.1188 0.2242 5.6793 6.5582
296 6.1188 0.2289 5.6701 6.5674
297 6.1188 0.2335 5.6611 6.5764
298 6.1188 0.2380 5.6522 6.5853
299 6.1188 0.2424 5.6436 6.5939
300 6.1188 0.2468 5.6350 6.6025
301 6.1188 0.2511 5.6267 6.6109
302 6.1188 0.2553 5.6184 6.6191
303 6.1188 0.2594 5.6103 6.6272
304 6.1188 0.2635 5.6023 6.6352
305 6.1188 0.2675 5.5945 6.6430
306 6.1188 0.2714 5.5867 6.6508
307 6.1188 0.2753 5.5791 6.6584
TAB7-16.SAS
options linesize=80;
data index;
infile "usind.dat" obs=271;
input date indx;
lagindx = lag(indx);
difindx = indx-lagindx;
lnindx = log(indx);
laglnind = lag(lnindx);
diflnind = lnindx-laglnind;
run;
proc arima;
identify var=lnindx(1) noprint;
estimate q=1 plot;
forecast out=fore lead=0;
run;
data convert;
set fore;
actual = exp(lnindx);
fitted = exp(forecast);
resid = actual - fitted;
er_ratio = resid/actual;
run;
*THE FOLLOWING TWO PROCEDURES GENERATE TABLE 7-16;
proc print data=convert;
var actual fitted resid er_ratio;
run;
proc means data=convert;
var actual fitted resid er_ratio;
run;
*THE FOLLOWING PROCEDURE GENERATES ALL BUT THE LAST LINE OF TABLE 7-13.;
*INFO CONTAINED IN THE LAST LINE OF TAB 7-13 CAN BE FOUND IN THE OUTPUT;
* OF THE ARIMA PROCEDURE ABOVE;
proc means data=index;
var indx difindx lnindx diflnind;
run;
run;
TAB7-16.LIS
1 The SAS System
1
14:42 Monday, April 6,
1998
ARIMA Procedure
Conditional Least Squares Estimation
Approx.
Parameter Estimate Std Error T Ratio Lag
MU 0.0055954 0.0028806 1.94 0
MA1,1 -0.32357 0.05789 -5.59 1
Constant Estimate = 0.00559543
Variance Estimate = 0.00128177
Std Error Estimate = 0.03580185
AIC = -1029.8487*
SBC = -1022.6518*
Number of Residuals= 270
* Does not include log determinant.
Correlations of the Estimates
Parameter MU MA1,1
MU 1.000 -0.000
MA1,1 -0.000 1.000
Autocorrelation Check of Residuals
To Chi Autocorrelations
Lag Square DF Prob
6 1.27 5 0.938 -0.003 -0.010 -0.005 -0.008 0.046 -0.047
12 6.91 11 0.806 -0.096 0.015 -0.035 -0.032 0.084 -0.038
18 10.17 17 0.896 0.006 -0.043 -0.045 0.027 -0.073 0.035
24 16.73 23 0.822 -0.079 -0.072 -0.063 0.019 -0.080 -0.004
30 20.59 29 0.873 0.004 0.057 0.092 0.028 0.011 -0.015
36 25.40 35 0.883 -0.023 -0.077 0.006 0.074 0.037 -0.047
42 27.87 41 0.941 0.042 0.067 0.006 -0.031 -0.010 0.022
48 33.61 47 0.929 0.030 -0.088 -0.012 -0.004 0.064 -0.068
1 The SAS System
2
14:42 Monday, April 6,
1998
ARIMA Procedure
Autocorrelation Plot of Residuals
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 0.0012818 1.00000 | |********************|
1 -4.443E-6 -0.00347 | . | . |
2 -0.0000126 -0.00982 | . | . |
3 -6.2247E-6 -0.00486 | . | . |
4 -9.7219E-6 -0.00758 | . | . |
5 0.00005918 0.04617 | . |*. |
6 -0.0000607 -0.04738 | .*| . |
7 -0.0001225 -0.09556 | **| . |
8 0.00001965 0.01533 | . | . |
9 -0.0000448 -0.03497 | .*| . |
10 -0.0000411 -0.03210 | .*| . |
11 0.0001073 0.08371 | . |** |
12 -0.0000486 -0.03793 | .*| . |
13 7.51882E-6 0.00587 | . | . |
14 -0.0000546 -0.04260 | .*| . |
15 -0.000058 -0.04527 | .*| . |
16 0.0000345 0.02691 | . |* . |
17 -0.000094 -0.07330 | . *| . |
18 0.00004545 0.03546 | . |* . |
19 -0.000101 -0.07882 | .**| . |
20 -0.0000929 -0.07249 | . *| . |
21 -0.0000811 -0.06329 | . *| . |
22 0.00002463 0.01921 | . | . |
23 -0.0001025 -0.07998 | .**| . |
24 -5.369E-6 -0.00419 | . | . |
"." marks two standard errors
1 The SAS System
3
14:42 Monday, April 6,
1998
ARIMA Procedure
Inverse Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 0.01349 | . | . |
2 0.04513 | . |*. |
3 0.03844 | . |*. |
4 0.02745 | . |*. |
5 -0.02367 | . | . |
6 0.07287 | . |*. |
7 0.12637 | . |*** |
8 0.00185 | . | . |
9 0.04085 | . |*. |
10 0.05165 | . |*. |
11 -0.06143 | .*| . |
12 0.03183 | . |*. |
13 0.03641 | . |*. |
14 0.07038 | . |*. |
15 0.04472 | . |*. |
16 0.00798 | . | . |
17 0.08585 | . |** |
18 -0.04354 | .*| . |
19 0.08734 | . |** |
20 0.06904 | . |*. |
21 0.07839 | . |** |
22 -0.00350 | . | . |
23 0.08625 | . |** |
24 0.01784 | . | . |
1 The SAS System
4
14:42 Monday, April 6,
1998
ARIMA Procedure
Partial Autocorrelations
Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
1 -0.00347 | . | . |
2 -0.00983 | . | . |
3 -0.00493 | . | . |
4 -0.00772 | . | . |
5 0.04603 | . |*. |
6 -0.04735 | .*| . |
7 -0.09537 | **| . |
8 0.01434 | . | . |
9 -0.03657 | .*| . |
10 -0.03660 | .*| . |
11 0.08733 | . |** |
12 -0.03251 | .*| . |
13 -0.00481 | . | . |
14 -0.04707 | .*| . |
15 -0.04399 | .*| . |
16 0.00793 | . | . |
17 -0.07050 | .*| . |
18 0.04852 | . |*. |
19 -0.09037 | **| . |
20 -0.07037 | .*| . |
21 -0.07901 | **| . |
22 0.00569 | . | . |
23 -0.09233 | **| . |
24 -0.01913 | . | . |
Model for variable LNINDX
Estimated Mean = 0.00559543
Period(s) of Differencing = 1.
Moving Average Factors
Factor 1: 1 + 0.32357 B**(1)
1 The SAS System
5
14:42 Monday, April 6,
1998
OBS ACTUAL FITTED RESID ER_RATIO
1 98.2 . . .
2 94.8 98.751 -3.9510 -0.04168
3 96.4 94.081 2.3193 0.02406
4 93.5 97.708 -4.2078 -0.04500
5 82.7 92.695 -9.9949 -0.12086
6 82.2 80.150 2.0502 0.02494
7 82.4 83.340 -0.9395 -0.01140
8 84.8 82.559 2.2411 0.02643
9 89.8 86.018 3.7819 0.04212
10 91.8 91.570 0.2301 0.00251
11 91.7 92.390 -0.6901 -0.00753
12 98.0 91.991 6.0089 0.06132
13 101.7 100.588 1.1116 0.01093
14 105.6 102.635 2.9650 0.02808
15 108.3 107.176 1.1244 0.01038
16 112.1 109.276 2.8239 0.02519
17 110.6 113.663 -3.0635 -0.02770
18 108.5 110.242 -1.7417 -0.01605
19 107.7 108.548 -0.8480 -0.00787
20 105.8 108.030 -2.2298 -0.02108
21 108.1 105.678 2.4219 0.02240
22 105.8 109.507 -3.7065 -0.03503
23 100.9 105.215 -4.3148 -0.04276
24 107.9 100.101 7.7994 0.07228
25 112.4 111.172 1.2282 0.01093
26 114.5 113.433 1.0668 0.00932
27 117.1 115.492 1.6083 0.01373
28 118.4 118.285 0.1148 0.00097
29 117.1 119.102 -2.0017 -0.01709
30 117.5 117.113 0.3870 0.00329
31 116.6 118.286 -1.6855 -0.01446
32 120.8 116.711 4.0890 0.03385
33 119.0 122.839 -3.8389 -0.03226
34 119.2 118.445 0.7554 0.00634
35 125.1 120.116 4.9843 0.03984
36 127.8 127.468 0.3321 0.00260
37 128.8 128.625 0.1747 0.00136
38 124.2 129.580 -5.3796 -0.04331
39 122.3 123.195 -0.8950 -0.00732
40 119.9 122.696 -2.7964 -0.02332
41 116.6 119.677 -3.0767 -0.02639
42 113.9 116.270 -2.3703 -0.02081
43 115.1 113.778 1.3217 0.01148
44 112.9 116.179 -3.2792 -0.02905
45 114.9 112.487 2.4134 0.02100
46 119.5 116.341 3.1589 0.02643
47 111.0 121.217 -10.2167 -0.09204
48 103.1 108.488 -5.3876 -0.05226
49 104.5 101.984 2.5162 0.02408
50 101.7 105.918 -4.2184 -0.04148
51 106.0 100.935 5.0654 0.04779
52 100.6 108.297 -7.6971 -0.07651
53 97.5 98.780 -1.2797 -0.01313
54 97.7 97.634 0.0657 0.00067
55 90.1 98.270 -8.1696 -0.09067
1 The SAS System
6
14:42 Monday, April 6,
1998
OBS ACTUAL FITTED RESID ER_RATIO
56 82.7 88.096 -5.39640 -0.065253
57 74.1 81.480 -7.38033 -0.099600
58 75.5 72.261 3.23865 0.042896
59 78.0 77.008 0.99161 0.012713
60 73.0 78.763 -5.76306 -0.078946
61 78.9 71.627 7.27325 0.092183
62 87.1 81.865 5.23515 0.060105
63 91.1 89.363 1.73676 0.019064
64 92.2 92.184 0.01648 0.000179
65 98.0 92.723 5.27729 0.053850
66 100.5 100.331 0.16910 0.001683
67 100.6 101.119 -0.51900 -0.005159
68 93.2 100.996 -7.79618 -0.083650
69 92.1 91.318 0.78187 0.008489
70 96.3 92.873 3.42737 0.035591
71 98.0 97.983 0.01743 0.000178
72 96.5 98.556 -2.05556 -0.021301
73 105.4 96.382 9.01810 0.085561
74 109.5 109.104 0.39624 0.003619
75 110.0 110.244 -0.24366 -0.002215
76 110.9 110.538 0.36194 0.003264
77 110.0 111.640 -1.64030 -0.014912
78 110.7 110.089 0.61130 0.005522
79 113.3 111.521 1.77921 0.015704
80 112.4 114.521 -2.12076 -0.018868
81 114.7 112.349 2.35088 0.020496
82 110.8 116.119 -5.31907 -0.048006
83 110.1 109.744 0.35601 0.003234
84 113.8 110.834 2.96613 0.026064
85 112.9 115.421 -2.52066 -0.022327
86 109.8 112.725 -2.92522 -0.026641
87 109.4 109.481 -0.08072 -0.000738
88 107.7 109.988 -2.28760 -0.021241
89 107.4 107.570 -0.17026 -0.001585
90 108.0 107.947 0.05271 0.000488
91 109.0 108.623 0.37684 0.003457
92 106.3 109.735 -3.43451 -0.032310
93 104.7 105.802 -1.10224 -0.010528
94 102.0 104.931 -2.93131 -0.028738
95 102.6 101.636 0.96372 0.009393
96 102.1 103.491 -1.39124 -0.013626
97 98.2 102.224 -4.02425 -0.040980
98 96.8 97.476 -0.67601 -0.006984
99 96.6 97.124 -0.52420 -0.005427
100 100.8 96.972 3.82792 0.037975
101 106.0 102.643 3.35660 0.031666
102 106.2 107.710 -1.51043 -0.014222
103 105.7 106.309 -0.60901 -0.005762
104 113.0 106.096 6.90431 0.061100
105 113.0 115.976 -2.97597 -0.026336
106 109.4 112.682 -3.28226 -0.030002
107 103.3 108.967 -5.66659 -0.054856
108 104.5 102.100 2.39997 0.022966
109 108.5 105.879 2.62064 0.024153
110 106.9 109.975 -3.07541 -0.028769
1 The SAS System
7
14:42 Monday, April 6,
1998
OBS ACTUAL FITTED RESID ER_RATIO
111 108.9 106.518 2.3822 0.02188
112 111.0 110.298 0.7024 0.00633
113 108.5 111.852 -3.3523 -0.03090
114 110.7 108.040 2.6602 0.02403
115 111.7 112.201 -0.5008 -0.00448
116 116.8 112.164 4.6357 0.03969
117 118.1 119.005 -0.9046 -0.00766
118 113.6 118.470 -4.8698 -0.04287
119 112.8 112.696 0.1036 0.00092
120 117.2 113.467 3.7333 0.03185
121 120.6 119.099 1.5014 0.01245
122 125.5 121.769 3.7307 0.02973
123 113.9 127.443 -13.5426 -0.11890
124 112.0 110.450 1.5498 0.01384
125 117.1 113.137 3.9626 0.03384
126 124.6 119.076 5.5239 0.04433
127 130.4 127.151 3.2489 0.02491
128 134.3 132.207 2.0934 0.01559
129 137.6 135.742 1.8582 0.01350
130 141.7 138.982 2.7178 0.01918
131 147.6 143.391 4.2092 0.02852
132 145.2 149.824 -4.6242 -0.03185
133 144.6 144.541 0.0590 0.00041
134 139.7 145.431 -5.7306 -0.04102
135 144.9 138.668 6.2317 0.04301
136 146.2 147.800 -1.6004 -0.01095
137 143.3 146.503 -3.2033 -0.02235
138 143.9 143.077 0.8231 0.00572
139 140.5 144.976 -4.4763 -0.03186
140 141.0 139.862 1.1382 0.00807
141 128.7 142.164 -13.4635 -0.10461
142 130.3 125.322 4.9780 0.03820
143 133.7 132.693 1.0069 0.00753
144 134.7 134.779 -0.0795 -0.00059
145 127.6 135.430 -7.8300 -0.06136
146 124.6 125.867 -1.2670 -0.01017
147 120.6 124.890 -4.2896 -0.03557
148 126.5 119.913 6.5871 0.05207
149 126.6 129.430 -2.8301 -0.02235
150 119.7 126.403 -6.7029 -0.05600
151 119.0 118.268 0.7319 0.00615
152 119.3 119.907 -0.6068 -0.00509
153 133.2 119.773 13.4274 0.10081
154 144.3 138.633 5.6672 0.03927
155 150.2 147.003 3.1969 0.02128
156 151.6 152.098 -0.4979 -0.00328
157 156.9 152.289 4.6110 0.02939
158 159.7 159.311 0.3894 0.00244
159 165.2 160.723 4.4770 0.02710
160 171.6 167.610 3.9896 0.02325
161 178.5 173.881 4.6186 0.02587
162 181.0 181.031 -0.0307 -0.00017
163 181.6 182.006 -0.4056 -0.00223
164 176.7 182.487 -5.7872 -0.03275
165 181.8 175.848 5.9518 0.03274
1 The SAS System
8
14:42 Monday, April 6,
1998
OBS ACTUAL FITTED RESID ER_RATIO
166 182.4 184.800 -2.3998 -0.01316
167 179.7 182.649 -2.9494 -0.01641
168 178.8 179.759 -0.9589 -0.00536
169 181.0 179.492 1.5077 0.00833
170 171.1 182.509 -11.4089 -0.06668
171 171.3 168.504 2.7964 0.01632
172 171.4 173.181 -1.7810 -0.01039
173 170.3 171.786 -1.4862 -0.00873
174 166.6 170.775 -4.1748 -0.02506
175 164.3 166.199 -1.8985 -0.01156
176 178.9 164.609 14.2912 0.07988
177 180.7 184.816 -4.1161 -0.02278
178 179.3 180.394 -1.0945 -0.00610
179 180.9 179.951 0.9486 0.00524
180 178.9 182.225 -3.3248 -0.01858
181 186.7 178.835 7.8649 0.04213
182 196.8 190.380 6.4195 0.03262
183 195.2 200.039 -4.8393 -0.02479
184 196.5 194.746 1.7540 0.00893
185 201.1 198.177 2.9233 0.01454
186 205.5 203.189 2.3112 0.01125
187 209.4 207.411 1.9893 0.00950
188 204.8 211.226 -6.4263 -0.03138
189 200.2 203.901 -3.7005 -0.01848
190 202.5 200.134 2.3662 0.01169
191 214.8 204.412 10.3878 0.04836
192 225.5 219.498 6.0023 0.02662
193 226.5 228.753 -2.2535 -0.00995
194 238.6 227.042 11.5575 0.04844
195 252.7 243.825 8.8753 0.03512
196 258.9 257.075 1.8252 0.00705
197 259.4 260.949 -1.5494 -0.00597
198 266.8 260.353 6.4466 0.02416
199 261.3 270.429 -9.1289 -0.03494
200 266.5 259.863 6.6373 0.02491
201 259.2 270.191 -10.9913 -0.04240
202 258.2 257.175 1.0248 0.00397
203 266.6 259.983 6.6169 0.02482
204 270.4 270.285 0.1150 0.00043
205 287.7 271.955 15.7453 0.05473
206 305.6 294.631 10.9686 0.03589
207 318.1 310.971 7.1290 0.02241
208 314.7 322.240 -7.5396 -0.02396
209 314.5 314.051 0.4492 0.00143
210 327.8 316.411 11.3890 0.03474
211 337.3 333.433 3.8673 0.01147
212 358.3 340.461 17.8394 0.04979
213 346.6 366.314 -19.7141 -0.05688
214 304.8 342.361 -37.5615 -0.12323
215 266.5 295.199 -28.6988 -0.10769
216 262.1 259.272 2.8282 0.01079
217 272.5 264.498 8.0024 0.02937
218 280.8 276.685 4.1153 0.01466
219 289.1 283.728 5.3722 0.01858
220 285.7 292.492 -6.7920 -0.02377
1 The SAS System
9
14:42 Monday, April 6,
1998
OBS ACTUAL FITTED RESID ER_RATIO
221 278.6 285.127 -6.5272 -0.02343
222 294.4 278.072 16.3283 0.05546
223 292.7 301.569 -8.8686 -0.03030
224 286.9 291.513 -4.6132 -0.01608
225 291.5 287.025 4.4755 0.01535
226 301.8 294.607 7.1931 0.02383
227 294.8 305.872 -11.0716 -0.03756
228 300.8 292.939 7.8613 0.02613
229 310.5 305.091 5.4091 0.01742
230 319.8 314.023 5.7772 0.01806
231 318.4 323.497 -5.0970 -0.01601
232 328.9 318.545 10.3546 0.03148
233 341.5 334.187 7.3134 0.02142
234 352.2 345.830 6.3699 0.01809
235 361.1 356.274 4.8260 0.01336
236 377.0 364.710 12.2895 0.03260
237 377.8 383.203 -5.4027 -0.01430
238 377.9 378.178 -0.2784 -0.00074
239 370.1 379.930 -9.8299 -0.02656
240 379.2 369.033 10.1667 0.02681
241 369.8 384.696 -14.8958 -0.04028
242 359.5 367.153 -7.6535 -0.02129
243 368.2 359.061 9.1386 0.02482
244 367.9 373.289 -5.3894 -0.01465
245 381.0 368.228 12.7725 0.03352
246 392.0 387.388 4.6116 0.01176
247 391.6 395.712 -4.1119 -0.01050
248 359.8 392.469 -32.6686 -0.09080
249 343.1 351.786 -8.6860 -0.02532
250 334.1 342.245 -8.1453 -0.02438
251 343.0 333.366 9.6337 0.02809
252 357.6 348.119 9.4812 0.02651
253 354.1 362.747 -8.6468 -0.02442
254 394.1 353.318 40.7820 0.10348
255 405.0 410.570 -5.5696 -0.01375
256 413.0 405.477 7.5234 0.01822
257 411.2 417.795 -6.5953 -0.01604
258 411.5 411.384 0.1162 0.00028
259 413.6 413.847 -0.2468 -0.00060
260 423.6 415.840 7.7595 0.01832
261 421.2 428.533 -7.3327 -0.01741
262 420.8 421.205 -0.4046 -0.00096
263 419.8 423.030 -3.2296 -0.00769
264 422.6 421.110 1.4900 0.00353
265 452.6 425.457 27.1428 0.05997
266 448.8 464.339 -15.5391 -0.03462
267 443.1 446.375 -3.2749 -0.00739
268 443.2 444.526 -1.3259 -0.00299
269 451.2 445.256 5.9437 0.01317
270 444.1 455.683 -11.5828 -0.02608
271 451.5 442.887 8.6132 0.01908
1 The SAS System
10
14:42 Monday, April 6,
1998
Variable N Mean Std Dev Minimum Maximum
---------------------------------------------------------------------
ACTUAL 271 188.0188192 107.2613249 73.0000000 452.6000000
FITTED 270 188.1843266 107.0411157 71.6267535 464.3390564
RESID 270 0.1671548 7.3016362 -37.5614793 40.7820133
ER_RATIO 270 -0.000580407 0.0360271 -0.1232332 0.1034814
---------------------------------------------------------------------
1 The SAS System
11
14:42 Monday, April 6,
1998
Variable N Mean Std Dev Minimum Maximum
---------------------------------------------------------------------
INDX 271 188.0188192 107.2613249 73.0000000 452.6000000
DIFINDX 270 1.3085185 7.7179630 -41.8000000 40.0000000
LNINDX 271 5.0950604 0.5151021 4.2904594 6.1150087
DIFLNIND 270 0.0056503 0.0375192 -0.1342816 0.1102104
---------------------------------------------------------------------
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