Forecasting

Document Sample
Forecasting Powered By Docstoc
					Module 4. Forecasting

       MGS3100




                    1
   Forecasting

                      Forecasting

Quantitative                               Qualitative

               Causal Model                              Expert Judgment

                                Trend                     Delphi Method

               Time series                                 Grassroots

                              Stationary

                                Trend

                         Trend + Seasonality                        2
   Quantitative Forecasting
         --Forecasting based on data and models
• Casual Models:

     Price
   Population
                     Causal            Year 2000
   Advertising       Model               Sales
     ……


• Time Series Models:
    Sales1999
    Sales1998       Time Series        Year 2000
    Sales1997         Model              Sales
     ……

                                                   3
             Causal forecasting

• Regression
   Find a straight line that fits the data best.
                12
                                                                            Best line!
                10

                 8

                 6

                 4

                 2

                 0
 Intercept           10   11   12   13   14   15   16   17   18   19   20



     y = Intercept + slope * x (= b0 + b1x)
     Slope = change in y / change in x
                                                                                         4
    Causal Forecasting Models

• Curve Fitting: Simple Linear Regression
  – One Independent Variable (X) is used to predict one
    Dependent Variable (Y): Y = a + b X
  – Given n observations (Xi, Yi), we can fit a line to the
    overall pattern of these data points. The Least
    Squares Method in statistics can give us the best a
    and b in the sense of minimizing (Yi - a - bXi)2:

        
    b    XiYi 
                    Xi  Yi  
                              /   Xi 2 
                                            ( Xi ) 2           
                                                                
                     n                     n                 
                                                             

    a
         Yi  b  Xi
          n        n
         Regression formula is an optional learning objective   5
• Curve Fitting: Simple Linear Regression
  – Find the regression line with Excel
     • Use Function:
       a = INTERCEPT(Y range; X range)
        b = SLOPE(Y range; X range)
     • Use Solver
     • Use Excel’s Tools | Data Analysis | Regression
• Curve Fitting: Multiple Regression
  – Two or more independent variables are used to
    predict the dependent variable:
    Y = b0 + b1X1 + b2X2 + … + bpXp
  – Use Excel’s Tools | Data Analysis | Regression


                                                        6
     Time Series Forecasting Process

Look at the data                  Forecast using one or           Evaluate the technique
(Scatter Plot)                    more techniques                 and pick the best one.

   Observations from the
                                      Techniques to try               Ways to evaluate
       scatter Plot

                              Heuristics - Averaging methods       MAD
Data is reasonably
                               Naive                              MAPE
stationary
                               Moving Averages                    Standard Error
(no trend or seasonality)
                               Simple Exponential Smoothing       BIAS
                                                                   MAD
                              Regression
                                                                   MAPE
Data shows a consistent        Linear
                                                                   Standard Error
trend                          Non-linear Regressions (not
                                                                   BIAS
                              covered in this course)
                                                                   R-Squared
                                                                   MAD
                              Classical decomposition
                                                                   MAPE
Data shows both a trend and    Find Seasonal Index
                                                                   Standard Error
a seasonal pattern             Use regression analyses to find
                                                                   BIAS
                              the trend component
                                                                   R-Squared
                                                                                         7
Evaluation of Forecasting Model
• BIAS - The arithmetic mean of the errors
          BIAS 
                    (Actual - Forecast)   Error
                            n                n
  –   n is the number of forecast errors
  –   Excel: =AVERAGE(error range)
• Mean Absolute Deviation - MAD
        MAD 
               | Actual - Forecast |   | Error |
                            n                  n
  –   No direct Excel function to calculate MAD



                                                      8
  Evaluation of Forecasting Model
• Mean Square Error - MSE
      MSE 
             (Actual - Forecast)   (Error)
                                    2             2


                          n                 n
   – Excel: =SUMSQ(error range)/COUNT(error range)
   – Standard error is square root of MSE
• Mean Absolute Percentage Error - MAPE
                     | Actual - Forecast|
                          Actual
                                          *100%
           M APE 
                                 n
• R2 - only for curve fitting model such as regression
• In general, the lower the error measure (BIAS, MAD,
  MSE) or the higher the R2, the better the forecasting
  model
                                                      9
         Stationary data forecasting

• Naïve
   I sold 10 units yesterday, so I think I will sell 10 units
    today.

• n-period moving average
    For the past n days, I sold 12 units on average.
     Therefore, I think I will sell 12 units today.

• Exponential smoothing
    I predicted to sell 10 units at the beginning of yesterday;
     At the end of yesterday, I found out I sold in fact 8 units.
     So, I will adjust the forecast of 10 (yesterday’s forecast)
     by adding adjusted error (α * error). This will compensate
     over (under) forecast of yesterday.
                                                                 10
 Naïve Model
• The simplest time series forecasting model
• Idea: “what happened last time (last year,
  last month, yesterday) will happen again
  this time”
• Naïve Model:
  –   Algebraic: Ft = Yt-1
      •   Yt-1 : actual value in period t-1
      •   Ft : forecast for period t
  –   Spreadsheet: B3: = A2; Copy down

                                               11
 Moving Average Model
• Simple n-Period Moving Average
              Sum of actual values in previous n periods
         F 
          t                       n
              Y     Y       Y
            =  t 1   t2           tn
                         n
• Issues of MA Model
  – Naïve model is a special case of MA with n = 1
  – Idea is to reduce random variation or smooth data
  – All previous n observations are treated equally (equal
    weights)
  – Suitable for relatively stable time series with no trend or
    seasonal pattern


                                                                  12
Smoothing Effect of MA Model




Longer-period moving averages (larger n) react to
actual changes more slowly
                                               13
Moving Average Model
• Weighted n-Period Moving Average
       F =w Y     w Y       w Y
        t  1 t 1   2 t 2       n t n
  – Typically weights are decreasing:
            w1>w2>…>wn
  – Sum of the weights = wi = 1
  – Flexible weights reflect relative importance of
    each previous observation in forecasting
  – Optimal weights can be found via Solver


                                                      14
Weighted MA: An Illustration

Month          Weight      Data
August          17%         130
September       33%         110
October         50%          90
November forecast:
FNov = (0.50)(90)+(0.33)(110)+(0.17)(130)
     = 103.4


                                            15
       Exponential Smoothing

• Concept is simple!
  – Make a forecast, any forecast
  – Compare it to the actual
  – Next forecast is
     • Previous forecast plus an adjustment
     • Adjustment is fraction of previous forecast error
  – Essentially
     • Not really forecast as a function of time
     • Instead, forecast as a function of previous actual and
       forecasted value



                                                            16
   Simple Exponential Smoothing
• A special type of weighted moving average
  – Include all past observations
  – Use a unique set of weights that weight recent observations
    much more heavily than very old observations:

   weight                                             0  1
           Decreasing weights                          
           given
             to older observations                      (1   )
                                                        (1   ) 2
                                                        (1   ) 3
                                                         
                                             Today           17
 Simple ES: The Model
Ft  Yt 1   (1   )Yt  2   (1   ) 2 Yt 3  
Ft  Yt 1  (1   )Yt  2   (1  a)Yt 3  

     Ft  Yt 1  (1   ) Ft 1
New forecast = weighted sum of last period
                     actual value and last period
forecast
– :      Smoothing constant
– Ft :    Forecast for period t
– Ft-1:   Last period forecast
– Yt-1:   Last period actual value
                                                   18
  Simple Exponential Smoothing
• Properties of Simple Exponential
  Smoothing
  – Widely used and successful model

  – Requires very little data

  – Larger , more responsive forecast; Smaller
    , smoother forecast (See Table 13.2)

  – “best”  can be found by Solver

  – Suitable for relatively stable time series

                                                 19
       Time Series Components

• Trend
  – persistent upward or downward pattern in a time series
• Seasonal
  – Variation dependent on the time of year
  – Each year shows same pattern
• Cyclical
  – up & down movement repeating over long time frame
  – Each year does not show same pattern
• Noise or random fluctuations
  – follow no specific pattern
  – short duration and non-repeating


                                                             20
Time Series Components


                               Cycle
Trend



           Random
           movement

    Time                               Time

Seasonal                        Trend with


                      Demand
pattern                         seasonal pattern




                                                   21
    Time                               Time
 Trend Model
• Curve fitting method used for time series data
  (also called time series regression model)
• Useful when the time series has a clear trend
• Can not capture seasonal patterns
• Linear Trend Model: Yt = a + bt
  – t is time index for each period, t = 1, 2, 3,…

                7
                6
                5
                4
                3
                2
                1
                0
                    1   2   3   4   5   6   7   8   9   10


                                                             22
             Pattern-based forecasting - Trend

• Regression – Recall Independent Variable X, which is now
  time variable – e.g., days, months, quarters, years etc.
     Find a straight line that fits the data best.
                12
                                                                            Best line!
                10

                 8

                 6

                 4

                 2

                 0
 Intercept           10   11   12   13   14   15   16   17   18   19   20


     y = Intercept + slope * x (= b0 + b1x)
     Slope = change in y / change in x

                                                                                         23
       Pattern-based forecasting – Seasonal

• Once data turn out to be seasonal,
  deseasonalize the data.
  – The methods we have learned (Heuristic methods and
    Regression) is not suitable for data that has
    pronounced fluctuations.
• Make forecast based on the deseasonalized data
• Reseasonalize the forecast
  – Good forecast should mimic reality. Therefore, it is
    needed to give seasonality back.


                                                       24
    Pattern-based forecasting – Seasonal
              Example (SI + Regression)

Actual data                        Deseasonalized data


                  Deseasonalize



                                                         Forecast




                   Reseasonalize


                                                           25
      Pattern-based forecasting – Seasonal

• Deseasonalization
  Deseasonalized data = Actual / SI

• Reseasonalization
  Reseasonalized forecast
              = deseasonalized forecast * SI




                                               26
       Seasonal Index

• What’s an index?
  – Ratio
  – SI = ratio between actual and average demand
• Suppose
  – SI for quarter demand is 1.20
     • What’s that mean?
     • Use it to forecast demand for next fall
  – So, where did the 1.20 come from?!



                                                   27
       Calculating Seasonal Indices

• Quick and dirty method of calculating SI
  – For each year, calculate average demand
  – Divide each demand by its yearly average
     • This creates a ratio and hence a raw index
     • For each quarter, there will be as many raw indices
       as there are years
  – Average the raw indices for each of the quarters
  – The result will be four values, one SI per quarter




                                                       28
       Classical decomposition

• Start by calculating seasonal indices
• Then, deseasonalize the demand
  – Divide actual demand values by their SI values
     y ’ = y / SI
  – Results in transformed data (new time series)
  – Seasonal effect removed
• Forecast
  – Regression if deseasonalized data is trendy
  – Heuristics methods if deseasonalized data is stationary
• Reseasonalize with SI

                                                      29
      Causal or Time series?

• What are the difference?

• Which one to use?




                               30
      Can you…

• describe general forecasting process?
• compare and contrast trend, seasonality and
  cyclicality?
• describe the forecasting method when data is
  stationary?
• describe the forecasting method when data
  shows trend?
• describe the forecasting method when data
  shows seasonality?

                                                 31

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:0
posted:5/8/2013
language:Latin
pages:31
gegouzhen12 gegouzhen12
About