Residual Correlation Diagnostics for x(1) 1.0 1.0 0.5 - 0.5 . PACE 0.0- -0.5 - -05- -1.0 -1.0 10 20 25 10 15 20 25 Lag Lag 1.0 - 0.5 -001- IACF 0.0 White Noise Prob -0.5- -1.0 10 15 20 25 10 20 25 Lag Lag Residual Normality Diagnostics for x(1) Distribution of Residuals QQ-Plot Normal 30000 - Kemel 60 - 20000- 10000 - 40 Percent Residual 20 -10000 -20000 -28000 -12000 4000 20000 36000 Residual QuantileAPPENDIX B Imports and Exports Imports 1300000- 1200000 1100000 1000000 900000 700000 600000 500000 400000 300000 200000 100000 1111 11 11 11 1 11 11 11 122222222222 222 9999999999999999999999999999999999999999900000000000000 566666666667777 7777778888886888999999999900000000001111 9012345678901234567890123456789012345678901234567890123 4444444444444444444444444444444444444444444444444444444 Date PLOT Imports - Exports Figure 2 Plot of Imports and ExportsMODEL 2 Maximum Likelihood Estimation Standard Approx Parameter Estimate Error Value Pr > Itl Lag MU 4384.1 2156.0 2.03 0.0420 MA1,1 0.03876 0.16870 0.23 0.8183 MA1 2 0.80232 0.13511 5.94 <.0001 n ar1 constant estimate variance std error aic sbc number of residuals autocorrelation check to lag chi-square df pr> Chisq Autocorrelations 4.96 2 0.0837 -0.036 -0.033 0.058 8 -0.088 0.079 -0.158 12 29.23 B 0.0003 0.086 0.174 -0.185 0.342 -0.118 -0.084 18 38.80 14 0.0004 -0.041 -0.203 0.057 0.023 0.122 0.126 24 47.71 20 0.0005 -0.180 0.145 0.035 -0.068 0.095 0.005MODEL 3 Maximum Likelihood Estimation Standard Approx Parameter Estimate Error t Value Pr > It Lag MU 4599.3 1178.4 3.90 <.0001 ma1 ar1 constant estimate variance std error aic sbc number of residuals autocorrelation check to lag chi-square df pr> Chisq Autocorrelations 181 0.1866 0.000 0.042 0.107 -0.041 0.134 -0.104 12 30.74 9 0.0003 0.123 0.212 -0.142 0.368- -0.086 -0.038 18 40.51 15 0.0004 -0.003 -0.165 0.089 0.043 0.139 0.148 24 48.90 31 0.0005 -0.144 0.161 0.051 -0.044 0.111 0.016 Unit Trust 300000 400000 300000 200000 100000 100090 -..NOON date PLOT Unit Trust Firm Difference Unit Tran Figure 1 Plot of the Unit Trust Series4.2 Figure 3 is a graphical representation of two time series data, Prices of Imports and Exports. It is clear that both series are non-stationary. Further, both series appear to trend together. When each series was differenced once, stationarity was achieved. This means that the two time series have the same order of integration, so we can proceed to test for cointegration. A regression analysis conducted to check whether the two time series are spurious are reported in Appendix B. Use these results to answer the following questions. I. Does the regression suffer from spurious regression phenomenon? Why or why not? Explain. II. Are prices of Imports and Exports cointegrated? [20 Marks] APPENDIX A MODEL 1 Maximum Likelihood Estimation Standard Approx Parameter Estimate Error t Value Pr > It| Lag MU 4567.1 1352.6 3.38 0.0007 MA1,1 0.40982 0.09219 4.45 <.0001 constant estimate variance std error aic sbc number of residuals autocorrelation check to lag chi-square pr> Chisq Autocorrelations 6 16.38 5 0.0058 -0.079 -0.080 0.198 -0.136 0.205 -0.193 12 46.54 11 <.0001 date plot first difference imports exports figure and engle-granger cointegration test type lag tau pr single mean trend ordinary least squares estimates sse dfe mse root sbc mae aicc mape hqc durbin-watson total r-square>