Let st be the log of the nominal exchange rate, pt be the log of the JPCPI, pi be the log of USCPI. Suppose that we generate the variables real exchange rate qt, by applying the following equation: qt = St + pm - pt In Eviews, we nominate Q the series real exchange rate qt. We obtain the following outputs: Table 11 Dependent Variable: D(Q) Method: Least Squares Sample (adjusted): 1991 M02 2015M12 Included observations: 299 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 0.001344 0.001530 0.878406 0.3804 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat 0.000000 0.000000 0.026461 0.208661 662.2271 1.403799 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. 0.001344 0.026461 -4.422924 -4.410547 -4.417970 Table 2 Heteroskedasticity Test: ARCH F-statistic Obs*R-squared 3.242495 35.68807 Prob. F(12,274) Prob. Chi-Square(12) 0.0002 0.0004 Table 3 Null Hypothesis: DQ is a martingale Sample: 1991 MO1 2015M12 Included observations: 298 (after adjustments) Heteroskedasticity robust standard error estimates User-specified lags: 24 8 16 Joint Tests Max Izl (at period 2)* Value 6.348720 df 298 Probability 0.0000 Individual Tests Period Var. Ratio 2 0.630864 4 0.407711 8 0.162653 16 0.101620 Std. Error 0.058143 0.115297 0.178910 0.257397 z-Statistic -6.348720 -5.137073 -4.680279 -3.490252 Probability 0.0000 0.0000 0.0000 0.0005 *Probability approximation using studentized maximum modulus with parameter value 4 and infinite degrees of freedom Test Details (Mean = 4.6068166836e-05) Var. Ratio Period 1 2 4 8 16 Variance 0.00099 0.00062 0.00040 0.00016 0.00010 0.63086 0.40771 0.16265 0.10162 Obs. 298 297 295 291 283 Table 4 Null Hypothesis: DQ is a martingale Sample: 1991 MO1 2015M12 Included observations: 298 (after adjustments) Heteroskedasticity robust standard error estimates User-specified lags: 24 8 16 Test probabilities computed using wild bootstrap: dist=normal, reps=1000, mng=kn, seed=1488230270 Joint Tests Max zl (at period 2) Value 6.348720 df 298 Probability 0.0000 Individual Tests Period Var. Ratio 2 0.630864 4 0.407711 8 0.162653 16 0.101620 Std. Error 0.058143 0.115297 0.178910 0.257397 z-Statistic -6.348720 -5.137073 -4.680279 -3.490252 Probability 0.0000 0.0000 0.0000 0.0020 Test Details (Mean = 4.6068166836e-05) Var. Ratio Period 1 2 4 8 16 Variance 0.00099 0.00062 0.00040 0.00016 0.00010 0.63086 0.40771 0.16265 0.10162 Obs. 298 297 295 291 283 Table 5 Null Hypothesis: DQ is a random walk Sample: 1991M01 2015M12 Included observations: 298 (after adjustments) Standard error estimates assume no heteroskedasticity User-specified lags: 24 8 16 Joint Tests Max Izl (at period 2)* Wald (Chi-Square) Value 6.372272 43.99192 df 298 4 Probability 0.0000 0.0000 Individual Tests Period Var. Ratio 2 0.630864 4 0.407711 8 0.162653 16 0.101620 Std. Error 0.057928 0.108374 0.171355 0.254984 Z-Statistic -6.372272 -5.465217 -4.886629 -3.523281 Probability 0.0000 0.0000 0.0000 0.0004 *Probability approximation using studentized maximum modulus with parameter value 4 and infinite degrees of freedom Test Details (Mean = 4.6068166836e-05) Var. Ratio Period 1 2 4 8 16 Variance 0.00099 0.00062 0.00040 0.00016 0.00010 0.63086 0.40771 0.16265 0.10162 Obs. 298 297 295 291 283 We want to test whether the real exchange rate qt is a random walk or a martingale. Describe the correct procedure for the test. Use and comment on the above tables (Table 1,2,3,4, and 5) to provide your answer. Let st be the log of the nominal exchange rate, pt be the log of the JPCPI, pi be the log of USCPI. Suppose that we generate the variables real exchange rate qt, by applying the following equation: qt = St + pm - pt In Eviews, we nominate Q the series real exchange rate qt. We obtain the following outputs: Table 11 Dependent Variable: D(Q) Method: Least Squares Sample (adjusted): 1991 M02 2015M12 Included observations: 299 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 0.001344 0.001530 0.878406 0.3804 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat 0.000000 0.000000 0.026461 0.208661 662.2271 1.403799 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. 0.001344 0.026461 -4.422924 -4.410547 -4.417970 Table 2 Heteroskedasticity Test: ARCH F-statistic Obs*R-squared 3.242495 35.68807 Prob. F(12,274) Prob. Chi-Square(12) 0.0002 0.0004 Table 3 Null Hypothesis: DQ is a martingale Sample: 1991 MO1 2015M12 Included observations: 298 (after adjustments) Heteroskedasticity robust standard error estimates User-specified lags: 24 8 16 Joint Tests Max Izl (at period 2)* Value 6.348720 df 298 Probability 0.0000 Individual Tests Period Var. Ratio 2 0.630864 4 0.407711 8 0.162653 16 0.101620 Std. Error 0.058143 0.115297 0.178910 0.257397 z-Statistic -6.348720 -5.137073 -4.680279 -3.490252 Probability 0.0000 0.0000 0.0000 0.0005 *Probability approximation using studentized maximum modulus with parameter value 4 and infinite degrees of freedom Test Details (Mean = 4.6068166836e-05) Var. Ratio Period 1 2 4 8 16 Variance 0.00099 0.00062 0.00040 0.00016 0.00010 0.63086 0.40771 0.16265 0.10162 Obs. 298 297 295 291 283 Table 4 Null Hypothesis: DQ is a martingale Sample: 1991 MO1 2015M12 Included observations: 298 (after adjustments) Heteroskedasticity robust standard error estimates User-specified lags: 24 8 16 Test probabilities computed using wild bootstrap: dist=normal, reps=1000, mng=kn, seed=1488230270 Joint Tests Max zl (at period 2) Value 6.348720 df 298 Probability 0.0000 Individual Tests Period Var. Ratio 2 0.630864 4 0.407711 8 0.162653 16 0.101620 Std. Error 0.058143 0.115297 0.178910 0.257397 z-Statistic -6.348720 -5.137073 -4.680279 -3.490252 Probability 0.0000 0.0000 0.0000 0.0020 Test Details (Mean = 4.6068166836e-05) Var. Ratio Period 1 2 4 8 16 Variance 0.00099 0.00062 0.00040 0.00016 0.00010 0.63086 0.40771 0.16265 0.10162 Obs. 298 297 295 291 283 Table 5 Null Hypothesis: DQ is a random walk Sample: 1991M01 2015M12 Included observations: 298 (after adjustments) Standard error estimates assume no heteroskedasticity User-specified lags: 24 8 16 Joint Tests Max Izl (at period 2)* Wald (Chi-Square) Value 6.372272 43.99192 df 298 4 Probability 0.0000 0.0000 Individual Tests Period Var. Ratio 2 0.630864 4 0.407711 8 0.162653 16 0.101620 Std. Error 0.057928 0.108374 0.171355 0.254984 Z-Statistic -6.372272 -5.465217 -4.886629 -3.523281 Probability 0.0000 0.0000 0.0000 0.0004 *Probability approximation using studentized maximum modulus with parameter value 4 and infinite degrees of freedom Test Details (Mean = 4.6068166836e-05) Var. Ratio Period 1 2 4 8 16 Variance 0.00099 0.00062 0.00040 0.00016 0.00010 0.63086 0.40771 0.16265 0.10162 Obs. 298 297 295 291 283 We want to test whether the real exchange rate qt is a random walk or a martingale. Describe the correct procedure for the test. Use and comment on the above tables (Table 1,2,3,4, and 5) to provide your