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Exchange Rate Predictability under the Present Value Model

VIEWS: 3 PAGES: 44

  • pg 1
									   Revisiting the Exchange Rate
Predictability in the Monetary Model

                  柯秀欣
         Department of Applied Economics
         National University of Kaohsiung


               May 31st, 2011


                                            1/44
Introduction
Motivation:
• Engel and West’s (2005) explanation for the near-random
  walk exchange rate under the present-value model:
     �������� = 1 − ���� ����1���� + ����1���� + ���� ����2���� + ����2���� + ������������ ��������+1
• A number of economic models fit into this present-value
  framework:
       Monetary Model
           1                   ∗            ∗                     ∗
  �������� =         �������� − �������� − ���� �������� − �������� + �������� − ������������ − ������������ − ������������
         1 + ����
                ����
           +          �������� ��������+1
             1 + ����
                                                                            2/44
Introduction
Motivation:
• After imposing the transversality condition, we have
                   ∞                                     ∞
                                       ′
  �������� = 1 − ����           ���� ���� �������� (a1 ����t+j ) + ����           ���� ���� �������� (a′2 ����t+j )   (1)
                  ���� =0                                 ���� =0

• xt+j includes observable and unobservable fundamentals




                                                                                                3/44
Introduction
Motivation:
                      ∞                                     ∞
                                          ′
     �������� = 1 − ����           ���� ���� �������� (a1 ����t+j ) + ����           ���� ���� �������� (a′2 ����t+j )   (1)
                     ���� =0                                 ���� =0
• Two assumptions for the near-random walk exchange rate
  (specifically for Δst):
  1. b is close to 1.
  2. either (1)                           and a2 = 0 or
              (2) no restrictions on                                 and
      →at least one fundamental has the unit root process


                                                                                               4/44
Introduction
Motivation:
• Suppose            and a2 = 0. For the model with
  univariate fundamental, the expectation of the k-
  difference exchange rate can be expressed as
                                     ∞                                  ����

  �������� ��������+���� − �������� = 1 − ���� ����           ���� ���� �������� Δ��������+����+���� +          1 − ���� ���� �������� Δ��������+����
                                    ���� =1                              ����=1

• Force from the fundamental:
• If the first-differenced fundamentals are not persistent, the
  exchange rate change is hard to predict.
  For instance, the fundamental is a random walk itself.

                                                                                                        5/44
Introduction
Motivation:
• Force from the discount factor:
• discount factor: one-quarter b = 0.99; one-year b = 0.974
      0.89; four-year b = 0.9716    0.61
• The larger the k of the k-period exchange rate change (i.e.,
  st+k – st ), the smaller the discount factor value for the
  exchange rate.
• In this case, one of the assumptions for the near-random
  walk exchange rate is violated.

                                                             6/44
Introduction
Motivation:
• Question:
1. While Engel and West’s (2005) assumptions implies that
   the short-horizon monetary exchange rate change is not
   predictable, will it be the case for the longer horizon
   exchange rate change? (Mark, 1995 or Kilian, 1999)

2. Which of the opposing forces would be stronger in the k-
   differences exchange rate?



                                                          7/44
Introduction
Method:
• Monte Carlo Simulations:
  We use 1000 Monte Carlo simulations to evaluate, in
  finite samples, the out-of-sample forecasting performance
  of the monetary model against the random walk model.

• Regression model:
  long-horizon error correction regression




                                                         8/44
Introduction
A glance of simulation results:
• The evidence of out-of-sample predictability is not
  consistently strong.
• The predictive power of the monetary model depends on
  whether the random walk null hypothesis includes a drift.
• Simulation results based on the asymptotic distribution
  and the bootstrap distribution can be very different.
• More credible results show that the out-of-sample
  predictability in the monetary model does not increase
  with the forecast horizon.


                                                         9/44
Introduction
Implication:
  1. The monetary model under Engel and West’s
  explanation would have the implication of the out-of-
  sample exchange rate predictability, yet the predictive
  power would not be strong even at long horizons.


  2. The force from the fundamental is stronger than the
  force from the fundamental and tends to increase at the
  longer forecast horizons.


                                                            10/44
Introduction
Literature Reviews:
   • Exchange Rages and Fundamentals:
     The random walk process outperforms any monetary models:
     Meese &Rogoff (JIE, 1983), Cheung, Chinn&Pascual (JIMF,
     2005)
   • Debate on the long-run predictability of exchange rates from
     fundamentals:
     Mark(AER, 1995), Mark and Sul (JIE, 2001)
     Kilian (JAE, 1999), Berkowitz&Giorgianni, (RES, 2001)

   • Related literatures: Engel, Wang, &Wu (2010)


                                                                    11/44
Outline
1.Introduction
2. The monetary model under Engel and West’s explanation
3. Monte Carlo experiment
    • Experiment design
    • Long-horizon regression test
    • Bootstrap algorithm
4. Monte Carlo experiment results
    • Data
    • Simulation results
5. Conclusions
                                                      12/44
The monetary model
• The present value model for the exchange rates:
                   ∞                                    ∞
                                       ′
  �������� = 1 − ����           ���� ���� �������� ����1 ���� t+j + ����           ���� ���� �������� (����′2 ���� ����+���� )
                  ���� =0                                ���� =0
• Two assumptions for the near-random walk behavior:
  1. b is close to 1.
  2. either (1)                        and a2 = 0 or
             (2) no restrictions on                         and
• We focus on the first assumptions on the fundamental in
  the discussion.

                                                                                             13/44
The monetary model
• Assuming all fundamental are observable to
  econometricians, the univariate monetary fundamental in
  the present-value model:
                               ∞
                       1                 ����          ����
              �������� =                                      �������� ��������+����
                     1 + ����            1 + ����
                              ���� =0
                                   ∞

                 = 1 − ����               ���� ���� �������� ��������+����
                                ���� =0
  where α is the money-demand interest semi-elasticity and
  f =(m - m*) - γ (y - y*) is the fundamental in the
  monetary model

                                                                         14/44
The monetary model
• The present-value equation can be rewritten as:
                                                    ∞

                             �������� = �������� +                ���� ���� �������� ��������+����
                                                  ���� =1
• We follow Mark (1995) researching into the k-differences
  exchange rate behavior.
• The expectation of the k-differences exchange rate in the
  present-value model:            ∞             ����

 �������� ��������+���� − �������� = �������� ��������+���� − �������� + 1 − ���� ����               ���� ���� �������� Δ��������+����+���� −          ���� ���� �������� Δ��������+����
                                                             ���� =1                              ����=1
                                   ∞                                 ����

                 = 1 − ���� ����             ���� ���� �������� Δ��������+����+���� +          1 − ���� ���� �������� Δ��������+����
                                 ���� =1                              ����=1
                                                                                                                       15/44
The monetary model
• Two forces affect the movement of the k-differences
  exchange rate:
    1. discount factor
    2. fundamental process
• If the fundamental is a random walk without the drift, the
  k-differences exchange rate in the present-value model is
  certainly unpredictable:
                                   ∞                                  ����

�������� ��������+���� − �������� = 1 − ���� ����           ���� ���� �������� Δ��������+����+���� +          1 − ���� ���� �������� Δ��������+����
                                  ���� =1                              ����=1
                =0
                                                                                               16/44
The monetary model

• For an AR model with the order larger than 1, it is
  difficult to derive algebraic expression because many
  parameters enter the derivation.


• We use the error-correction long-run regression model as
  many empirical works did:
               ��������+���� − �������� = �������� + �������� �������� + ��������+����
                            �������� = �������� − ��������

                                                             17/44
The monetary model

• The long-run regression is valid, or is not spurious, on the
  basis of the present-value model (Engel et al. 2010).


• We implement Monte Carlo experiments to investigate
  the out-of-sample k-differences exchange rate behavior.




                                                           18/44
Monte Carlo experiment
3.1 Experiment design
• Simulate the near-random walk exchange rates by the
  equation:
                                 ∞

                �������� = �������� +           ���� ���� �������� ��������+����
                                ���� =1

• We need to simulate Δft and then simulate st.
• In the simulation of Δft , we do not contain an intercept in
  the AR process and therefore have the initial value for the
  simulation process to be zero.
• The first 1500 time steps are discarded.

                                                              19/44
Monte Carlo experiment
3.1 Experiment design
                  ∞

• To obtain              ���� ���� �������� Δ��������+����   , we transform the AR model into
                 ���� =1
  an VAR model for the first-differenced fundamental.

• For the Δft ~ AR(p) process, we express it by
      Δ ��������              ����1        ����2       ⋯   ��������−1   ��������    Δ ��������−1       ��������
    Δ ��������−1               1          0        ⋯      0      0      Δ ��������−2        0
         ⋮       =         0          1        ⋯      0      0           ⋮       + ⋮
   Δ ��������−����+2             ⋮          ⋮        ⋱      ⋮      ⋮     Δ ��������−����+1      0
   Δ ��������−����+1             0          0        ⋯      1      0      Δ ��������−����       0


                                                                                          20/44
Monte Carlo experiment
3.1 Experiment design
• To simplify the notation,
              Δ ��������            ����1   ����2   ⋯   ��������−1   ��������                ��������
            Δ ��������−1             1     0    ⋯      0      0                   0
  �������� ≡         ⋮     ; ���� ≡    0     1    ⋯      0      0     and �������� ≡    ⋮
           Δ ��������−����+2           ⋮     ⋮    ⋱      ⋮      ⋮                   0
           Δ ��������−����+1           0     0    ⋯      1      0                   0

• Δft becomes a VAR(1) model:
                   �������� = ������������−1 + ��������



                                                                             21/44
Monte Carlo experiment
3.1 Experiment design
• Then,    ∞

                   ���� ���� �������� ��������+���� = ���� − ��������   −1
                                                         ����������������
           ���� =1
• Use a selection vector, we have
           ∞

                  ���� ���� �������� Δ��������+���� = 1, 0, ⋯ ,0 ���� − ��������        −1
                                                                         ����������������
          ���� =1

  and then obtain ft by the cumulative sum of simulated Δft.
• Discount factor b is 0.97 and the length of the series is
  identical to the real data.
                                                                                    22/44
Monte Carlo experiment
3.2 Long-horizon regression
• The regression test:
            ����0 : ��������+���� − �������� = �������� + ��������+���� , ���� =1, 8, 16
           ����1 : ��������+���� − �������� = �������� + �������� �������� + ��������+����   ( βk > 0 )

• Out-of-sample test statistics:
   Diebold-Mariano (DM) statistic and Theil U-statistic
• The prediction is based on the recursive estimation, and
  the number of predictions is 32.
• Use both of the asymptotic distribution and the bootstrap
  percentile distribution for the test inferences.
                                                                            23/44
Monte Carlo experiment
3.3 Bootstrap algorithm
Step 1: Given the simulated fundamental and the simulated
   exchange rate , where indicates the i-th batch of the simulated
   sequence (fi,t, si,t) and i= 1, 2, …, 1000, estimate the
   coefficients for the alternative hypothesis in model:



  and construct critical values for the test statistics, DM20, DMA,
  and Theil U for each i.




                                                                24/44
Monte Carlo experiment
3.3 Bootstrap algorithm
Step 2: To bootstrap DGP for                    , we first impose
   the constraint of the null hypothesis, and the regression
   equations of Δsi,t and zi,t are:




  The lag length of zi,t is selected by the AIC with the maximum
  length of lag being equal to 8. The innovation terms are
  assumed to be i.i.d. distributed. Then, estimate the coefficients
  in these two equations by the OLS method, correct the bias in
  the lag estimates ( ) of the error correction equation zi,t.
                                                                    25/44
Monte Carlo experiment
3.3 Bootstrap algorithm
Step 3: Based on the fitted model, generate a sequence of pseudo
   observation        of the same length as the simulated data.
   Under the null hypothesis that the exchange rate is a random
   walk with a drift, the bootstrap DGP is:




  The initial value specified for the process       is zero for
  j=1,2, …, q and discard the first 500 transients. The is
  generated by the cumulative sum of the realization of the
  bootstrap DGP. Repeat this step 999 times.
                                                                  26/44
Monte Carlo experiment
3.3 Bootstrap algorithm
Step 4: For each of the 999 bootstrap replications        , re-
   estimate the regression coefficients in the long-horizon
   regression equation:



   and construct the bootstrapping test statistics.
Step 5: Use the 999 bootstrapping test statistics from step 4 to
   construct a bootstrapping empirical distribution. Then,
   determine the p-value of the test statistic in step 1.



                                                                   27/44
Monte Carlo experiment results
4.1 Data
• The fundamental in the money income model:


• Canada and Japan: 1973:Q1 ~ 2008:Q3 (143
  observations );
  the United Kingdom: 1973:Q1 ~ 2006:Q4 (136
  observations);
  Switzerland: 1974:Q4 ~ 2008:Q2 (135 observations)

• The data resource is IMF-IFS.
                                                      28/44
Monte Carlo experiment results
4.1 Data
• The augmented Dickey-Fuller test with an intercept but
  without the time trend shows that all ft’s have the I(1)
  process

• The process of the monetary fundamental applied to the
  Monte Carlo experiment is consistent with the assumption
  of the present-value model for the near-random walk
  exchange rate.



                                                             29/44
Table 1. OLS estimates of lag parameters for the AR(p) first-differenced fundamental
                                         (a) Canada
  p           AR(1)             AR(4)             AR(8)            AR(AIC=4)
  1           0.362              0.290             0.252             0.290
  2            -                -0.021            -0.111             -0.021
  3            -                 0.323             0.311             0.323
  4            -                 0.016            -0.090             0.016
  5            -                  -                0.274               -
  6            -                  -                0.074               -
  7            -                  -                0.089               -
  8            -                  -               -0.136               -
                                         (b) Japan
  p           AR(1)             AR(4)             AR(8)            AR(AIC=3)
  1           0.148             0.051              0.049            0.0458
  2            -                0.162              0.134            0.1510
  3            -                0.188              0.140            0.1566
  4            -                0.144              0.120              -
  5            -                 -                 0.071              -
  6            -                 -                 0.062              -
  7            -                 -                 0.190              -
  8            -                 -                -0.127                -
                                                                                       30/44
Table 1. OLS estimates of lag parameters for the AR(p) first-differenced fundamental

                                       (c) Switzerland
  p            AR(1)             AR(4)              AR(8)          AR(AIC=1)
  1            0.326              0.285              0.288           0.326
  2              -                0.058              0.065             -
  3              -                0.101              0.089             -
  4              -                0.013              0.026             -
  5              -                  -               -0.075             -
  6              -                  -               -0.026             -
  7              -                  -                0.029             -
  8              -                  -               -0.013             -
                                      (d) United Kingdom
  p            AR(1)             AR(4)              AR(8)          AR(AIC=7)
  1            -0.412            -0.115              0.132           0.081
  2              -               -0.104             -0.026           -0.087
  3              -               -0.129             -0.058           -0.022
  4              -                0.788              0.584           0.752
  5              -                  -               -0.244           -0.264
  6              -                  -               -0.075           -0.067
  7              -                  -               -0.066           -0.162
  8              -                  -                0.243             -
                                                                                       31/44
     Table 2: Rejecting rates under H0: random walk with a drift in the exchange rate – asymptotic distribution
                                                        (a) Canada
              AR(1)                       AR(4)                       AR(8)                      AR(AIC)
 k      DM20 DMA      U             DM20 DMA      U             DM20 DMA      U             DM20 DMA      U
1       0.006 0.006 0.000           0.008 0.008 0.000           0.016 0.009 0.000           0.008 0.008 0.000
8       0.030 0.011 0.000           0.017 0.014 0.000           0.023 0.024 0.000           0.017 0.014 0.000
16      0.030 0.010 0.000           0.033 0.022 0.000           0.039 0.034 0.000           0.033 0.022 0.000
                                                         (b) Japan
              AR(1)                       AR(4)                       AR(8)                      AR(AIC)
 k      DM20 DMA      U             DM20 DMA      U             DM20 DMA      U             DM20 DMA      U
1       0.008 0.006 0.000           0.011 0.004 0.000           0.007 0.008 0.000           0.016 0.009 0.000
8       0.025 0.013 0.000           0.033 0.028 0.000           0.026 0.024 0.000           0.027 0.021 0.000
16      0.026 0.012 0.000           0.026 0.018 0.000           0.031 0.027 0.000           0.023 0.019 0.000
                                                      (c) Switzerland
              AR(1)                       AR(4)                       AR(8)                      AR(AIC)
 k      DM20 DMA      U             DM20 DMA      U             DM20 DMA      U             DM20 DMA      U
1       0.013 0.007 0.000           0.012 0.010 0.000           0.013 0.007 0.000           0.013 0.007 0.000
8       0.039 0.017 0.000           0.033 0.024 0.000           0.027 0.015 0.000           0.039 0.017 0.000
16      0.032 0.012 0.000           0.035 0.023 0.000           0.024 0.015 0.000           0.032 0.012 0.000
                                                   (d) United Kingdom
              AR(1)                       AR(4)                       AR(8)                      AR(AIC)
 k      DM20 DMA      U             DM20 DMA      U             DM20 DMA      U             DM20 DMA      U
1       0.009 0.005 0.000           0.009 0.003 0.000           0.009 0.009 0.000           0.017 0.013 0.000
8       0.029 0.015 0.000           0.038 0.031 0.000           0.028 0.023 0.000           0.023 0.015 0.000
16      0.034 0.010 0.000           0.040 0.030 0.000           0.038 0.030 0.000           0.046 0.039 0.000
                                                                                                                  32/44
     Table 3: Rejecting rates under H0: random walk with a drift in the exchange rate – bootstrap distribution
                                                       (a) Canada
             AR(1)                       AR(4)                        AR(8)                         AR(AIC)
 k     DM20 DMA      U             DM20 DMA      U              DM20 DMA      U             DM20     DMA     U
1      0.099 0.097 0.102           0.121 0.121 0.120            0.102 0.101 0.099           0.121    0.121 0.120
8      0.102 0.100 0.099           0.088 0.087 0.091            0.078 0.077 0.079           0.088    0.087 0.091
16     0.095 0.097 0.102           0.091 0.097 0.098            0.080 0.081 0.079           0.091    0.097 0.098
                                                        (b) Japan
             AR(1)                       AR(4)                        AR(8)                         AR(AIC)
 k     DM20 DMA      U             DM20 DMA      U              DM20 DMA      U             DM20     DMA     U
1      0.089 0.089 0.090           0.118 0.117 0.116            0.083 0.086 0.082           0.108    0.108 0.112
8      0.107 0.110 0.110           0.093 0.094 0.093            0.094 0.094 0.090           0.106    0.108 0.108
16     0.129 0.125 0.124           0.091 0.097 0.103            0.080 0.079 0.084           0.089    0.088 0.087
                                                     (c) Switzerland
             AR(1)                       AR(4)                        AR(8)                         AR(AIC)
 k     DM20 DMA      U             DM20 DMA      U              DM20 DMA      U             DM20     DMA     U
1      0.090 0.087 0.092           0.098 0.102 0.098            0.087 0.090 0.089           0.090    0.087 0.092
8      0.096 0.096 0.101           0.091 0.096 0.090            0.085 0.086 0.078           0.096    0.096 0.101
16     0.109 0.102 0.105           0.078 0.078 0.083            0.083 0.077 0.087           0.109    0.102 0.105
                                                   (d) United Kingdom
             AR(1)                       AR(4)                        AR(8)                         AR(AIC)
 k     DM20 DMA      U             DM20 DMA      U              DM20 DMA      U             DM20     DMA     U
1      0.088 0.092 0.089           0.096 0.097 0.101            0.103 0.103 0.103           0.123    0.126 0.126
8      0.106 0.101 0.114           0.075 0.069 0.085            0.071 0.071 0.097           0.043    0.040 0.068
16     0.115 0.110 0.114           0.070 0.063 0.091            0.060 0.050 0.089           0.058    0.043 0.061
                                                                                                                   33/44
Monte Carlo experiment
Under the H0: the exchange rate change is a random
 walk with a drift
• The predictive ability of the monetary model is little.

• The simulation results based on the asymptotic
  distribution shows that predictability tends to increase
  with forecast horizons, whereas the results based on the
  bootstrap distribution shows different pattern.

• Out-of-sample exchange rate predictability may occur in
  the middle run forecast horizon.
                                                            34/44
Monte Carlo experiment
Under the H0: the exchange rate change is a random
walk with a drift
• The rejecting rates of the U statistic are zero based on the
  asymptotic F distribution.

• We conjecture that it is due to the contemporaneously
  correlation between the prediction errors in two models.
  In the case of the contemporaneously correlation, using
  the F-distribution will result in accepting too often the
  null hypothesis (Mizrach, 1992).


                                                           35/44
Monte Carlo experiment
Long-horizon regression test:
• In literature, it is argued that whether to contain a drift in
  the random walk as the null does not come from theory,
  but instead from peeking at the data (Engel et al., 2007).

• The regression test:
                 ����0 : ��������+���� − �������� = ��������+���� , ���� =1, 8, 16
                 ����1 : ��������+���� − �������� = �������� �������� + ��������+����



                                                                 36/44
     Table 4: Rejecting rates under H0: driftless random walk in the exchange rate – asymptotic distribution
                                                      (a) Canada
            AR(1)                        AR(4)                       AR(8)                      AR(AIC)
 k    DM20 DMA      U              DM20 DMA      U             DM20 DMA      U             DM20 DMA      U
1     0.167 0.126 0.000            0.069 0.045 0.000           0.051 0.035 0.000           0.069 0.045 0.000
8     0.329 0.323 0.011            0.113 0.109 0.001           0.081 0.079 0.002           0.113 0.109 0.001
16    0.391 0.396 0.116            0.164 0.170 0.038           0.107 0.105 0.030           0.164 0.170 0.038
                                                       (b) Japan
            AR(1)                        AR(4)                       AR(8)                      AR(AIC)
 k    DM20 DMA      U              DM20 DMA      U             DM20 DMA      U             DM20 DMA      U
1     0.253 0.186 0.000            0.102 0.076 0.000           0.078 0.057 0.000           0.130 0.088 0.000
8     0.401 0.405 0.028            0.167 0.162 0.011           0.122 0.119 0.004           0.234 0.229 0.007
16    0.465 0.477 0.185            0.229 0.232 0.050           0.160 0.167 0.043           0.284 0.294 0.078
                                                    (c) Switzerland
            AR(1)                        AR(4)                       AR(8)                      AR(AIC)
 k    DM20 DMA      U              DM20 DMA      U             DM20 DMA      U             DM20 DMA      U
1     0.013 0.007 0.000            0.013 0.007 0.000           0.007 0.004 0.000           0.013 0.007 0.000
8     0.057 0.052 0.000            0.037 0.030 0.000           0.035 0.030 0.000           0.057 0.052 0.000
16    0.077 0.085 0.008            0.046 0.046 0.004           0.058 0.060 0.008           0.077 0.085 0.008
                                                  (d) United Kingdom
            AR(1)                        AR(4)                       AR(8)                      AR(AIC)
 k    DM20 DMA      U              DM20 DMA      U             DM20 DMA      U             DM20 DMA      U
1     0.052 0.029 0.000            0.067 0.040 0.000           0.045 0.031 0.000           0.125 0.081 0.000
8     0.147 0.142 0.001            0.132 0.119 0.003           0.099 0.093 0.001           0.269 0.260 0.006
16    0.172 0.179 0.027            0.176 0.179 0.031           0.137 0.141 0.023           0.322 0.337 0.089
                                                                                                               37/44
     Table 5: Rejecting rates under H0: driftless random walk in the exchange rate – bootstrap distribution
                                                      (a) Canada
            AR(1)                       AR(4)                       AR(8)                       AR(AIC)
 k    DM20 DMA      U             DM20 DMA      U             DM20 DMA      U              DM20 DMA      U
1     0.686 0.674 0.665           0.448 0.444 0.431           0.325 0.322 0.314            0.448 0.444 0.431
8     0.677 0.677 0.686           0.382 0.382 0.382           0.251 0.252 0.249            0.382 0.382 0.382
16    0.622 0.618 0.652           0.342 0.342 0.354           0.233 0.233 0.235            0.342 0.342 0.354
                                                       (b) Japan
            AR(1)                       AR(4)                       AR(8)                       AR(AIC)
 k    DM20 DMA      U             DM20 DMA      U             DM20 DMA      U              DM20 DMA      U
1     0.790 0.782 0.773           0.533 0.531 0.513           0.455 0.451 0.430            0.603 0.595 0.577
8     0.783 0.784 0.799           0.450 0.452 0.449           0.396 0.396 0.396            0.579 0.579 0.580
16    0.733 0.729 0.763           0.432 0.430 0.435           0.385 0.386 0.388            0.517 0.519 0.535
                                                    (c) Switzerland
            AR(1)                       AR(4)                       AR(8)                       AR(AIC)
 k    DM20 DMA      U             DM20 DMA      U             DM20 DMA      U              DM20 DMA      U
1     0.132 0.133 0.134           0.119 0.117 0.117           0.123 0.122 0.120            0.132 0.133 0.134
8     0.170 0.172 0.166           0.103 0.103 0.105           0.120 0.119 0.120            0.170 0.172 0.166
16    0.153 0.153 0.152           0.108 0.109 0.100           0.122 0.123 0.111            0.153 0.153 0.152
                                                 (d) United Kingdom
            AR(1)                       AR(4)                       AR(8)                       AR(AIC)
 k    DM20 DMA      U             DM20 DMA      U             DM20 DMA      U              DM20 DMA      U
1     0.266 0.267 0.270           0.343 0.343 0.346           0.232 0.230 0.235            0.500 0.497 0.499
8     0.325 0.325 0.352           0.317 0.314 0.342           0.246 0.241 0.258            0.540 0.541 0.576
16    0.314 0.313 0.331           0.317 0.316 0.329           0.237 0.237 0.250            0.506 0.506 0.532
                                                                                                               38/44
Summary of the simulation results
• The evidence of out-of-sample exchange rate
  predictability is not consistently strong.

• The predictive power of the monetary model depends on
  whether the random walk null hypothesis includes a drift.

• There is some evidence of predictability at the middle run
  forecast horizon.




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Summary of the simulation results
• Simulation results based on the asymptotic distribution
  and the bootstrap distribution can be very different.

• Simulation results based on the bootstrap distribution
  show that the out-of-sample predictability in the monetary
  model does not increase with the forecast horizon.




                                                            40/44
Conclusion Remarks
• We draw the conclusion form the simulation results based
  on the bootstrap distribution because the asymptotic
  results is very likely distorted by the small sample bias.

• The evidence of the out-of-sample exchange rate
  predictability in the standard monetary model under
  Engel and West’s explanation is not significantly strong.




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Conclusion Remarks
• We infer that the monetary model under Engel and West’s
  assumptions would have the implication of out-of-sample
  predictability, yet the predictive power would not be
  strong even at the long horizon.

• The force from the fundamental is stronger than the force
  from the discount factor and tends to increase at the
  longer forecast horizons.




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Conclusion Remarks
• The findings of Clark and West (2006) may help resolve
  the low rejecting rate.

• Clark and West (2006): the sample MSPE of a linear
  alternative model is expected to be greater than that of a
  zero-mean-martingale-difference null model.




                                                           43/44
Thank you for your attention.




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