I. To examine the volatility clustering phenomena in the foreign exchange rate market, a two- step test has been conduct

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I To Examine The Volatility Clustering Phenomena In The Foreign Exchange Rate Market A Two Step Test Has Been Conduct 1 (184.35 KiB) Viewed 21 times

I. To examine the volatility clustering phenomena in the foreign exchange rate market, a two- step test has been conducted on the first logarithmic difference of exchange rate between German Mark and U.S. Dollar (D_DM). The analysis results are shown as follows: Heteroskedasticity Test: ARCH Dependent Variable: D_DM Method: ARMA Maximum Likelihood (BFGS) Date: 08/07/20 Time: 11:08 Sample: 21500 Included observations: 1499 Convergence achieved after 3 iterations. Coefficient covariance computed using outer product of gradients Std. Error t-Statistic Variable AR(1) SIGMASQ R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) Inverted AR Roots II. Coefficient -0.000260 0.000194 -1.339953 0.1805 -0.055969 0.022136 -2.528450 0.0116 5.76E-05 1.47E-06 39.24557 0.0000 0.003136 Mean dependent var 0.001803 S.D. dependent var 0.007597 Akaike info criterion 0.086349 Schwarz criterion 5189.562 Hannan-Quinn criter. 2.353203 Durbin-Watson stat 0.095416 - 06 Prob. -0.000260 0.007604 -6.920029 -6.909397 -6.916068 1.993645 F-statistic Obs*R-squared Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 08/07/20 Time: 11:11 Sample (adjusted): 31500 Included observations: 1498 after adjustments Coefficient 5.16E-05 0.104543 Variable C RESID^2(-1) 16.52980 Prob. F(1,1496) 16.37101 Prob. Chi-Square(1) R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) Std. Error 3.56E-06 0.025713 t-Statistic 14.48596 4.065685 0.010929 Mean dependent var 0.010267 S.D. dependent var 0.000125 Akaike info criterion 2.35E-05 Schwarz criterion 11333.65 Hannan-Quinn criter. 16.52980 Durbin-Watson stat 0.000050 Use the relevant statistics from the above tables, explain whether volatility clustering is a significant phenomenon for D_DM. And conclude whether ARCH models are appropriate for examining the behavior of the exchange rate series. (2 Marks) Three models of the ARCH/GARCH types are considered for the D_DM. Based on the analysis results shown in the following tables, explain which model is most appropriate one. (3 Marks) 0.0001 0.0001 Prob. 0.0000 0.0001 5.76E-05 0.000126 -15.12903 -15.12194 -15.12639 2.019651 MODEL I Dependent Variable: D_DM Method: ML ARCH- Normal distribution (BFGS/Marquardt steps) Date: 08/07/20 Time: 11:13 Sample (adjusted): 31500 Included observations: 1498 after adjustments Convergence achieved after 12 iterations Coefficient covariance computed using outer product of gradients Presample variance: backcast (parameter = 0.7) GARCH=C(3) C(4)"RESID(-1)^2 Variable C AR(1) C RESID(-1)^2 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Inverted AR Roots MODEL 3 Coefficient. Std. Error Prob.. -0.000393 0.000184 -2.139335 0.0324 -0.067079 0.028668 -2.339882 0.0193 Variance Equation 4.68E-05 1.77E-06 26.41991 0.0000 0.194876 0.021639 9.005742 0.0000 0.002655 Mean dependent var -0.000258 0.001988 S.D. dependent var 0.007606 0.007599 Akaike info criterion -6.952399 0.086376 Schwarz criterion -6.938215 5211.347 Hannan-Quinn criter -6.947115 1.969580 -.07 Dependent Variable: D DM Method: ML ARCH- Normal distribution (BFGS/Marquardt steps) Date: 08/07/20 Time: 11:15 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Inverted AR Roots III Sample (adjusted): 31500 Included observations: 1498 after adjustments Convergence achieved after 33 iterations Coefficient covariance computed using outer product of gradients Presample variance: backcast (parameter = 0.7) GARCH=C(3) C(4) RESID(-1)^2 C(5) RESID(-12*(RESID(-1)-0). C(6) GARCH(-1) Variable С AR(1) RESID(-1)^2 RESID(-1)^2*(RESID(-1)-0) GARCH(-1) 2-Statistic Coefficient Std. Error 2-Statist Prob. -0.000520 0.000160 -3.247433 0.0012 -0.079606 0.029584 -2.785013 0.0054 Variance Equation 7.60E-07 2.70E-07 2.809456 0 065232 0.011844 5.507768 0.059687 0.016741 3.565283 S 0.899439 0.013137 68.46483 0.001191 Mean dependent var 0 000523 0.007604 8.D. dependent var 0007604 Akaike info criterion 0.086503 Schwarz criterion 5299.392 Hannan-Quinn criter. 1.941210 -.09 0.0050 0.0000 0.0004 0.0000 -0.000258 0.007606 01 -7.067279 -7.046003 -7.059352 MODEL 2 Dependent Variable: D_DM Method: ML ARCH- Normal distribution (BFGS/Marquardt steps) Date: 08/07/20 Time: 11:14 Sample (adjusted): 31500 Included observations: 1498 after adjustments Convergence achieved after 27 iterations Coefficient covariance computed using outer product of gradients Presample variance: backcast (parameter = 0.7) GARCH=C(3) + C(4)*RESID(-1)^2 + C(5)*GARCH(-1) Std. Error Variable C AR(1) C RESID(-1)^2 GARCH(-1) R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Inverted AR Roots Coefficient z-Statistic -0.000412 0.000148 -2.780930 0.0054 -0.077550 -2.658784 0.0078 0.029167 Variance Equation 1.19E-06 3.42E-07 3.476185 0.0005 0.107640 0.012296 8.753966 0.0000 0.877283 0.014597 60.10056 0.0000 -0.000258 0.007606 -7.062591 -7.044861 -7.055986 0.002196 Mean dependentvar 0.001529 SD. dependent var 0.007600 Akaike info criterion 0.086416 Schwarz criterion 5294.881 Hannan-Quinn criter. 1.947314 Prob -.08 Based on the Three models of the ARCH/GARCH type in part (II) above, explain whether good and bad news have symmetric effects on D_DM. (2 Marks)