5. A researcher is investigating the realtionship between US GDP and Consumption growth. The data, which...

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5. A researcher is investigating the realtionship between US GDP and Consumption growth. The data, which has been collected quarterly and is from 1960 to 2019, is plotted below: GR US CU and Consumption Growth Hataw 1960 to 2015 1970 1800 1200 2000 Conaryton 2010 2000 The researcher has decided to fit VAR(P) models to this bivariate system and has obtained Information Criteria measures for P=1 to 10. These are presented in the table below: P 1 2 3 4 5 6 7 8 9 10 AIC(P) HQ(P) SC(P) FPE(P) -1.429 -1.393 -1.339 0.239 -1.604 -1.543 -1.453 0.201 -1.720 -1.635 -1.509 0.179 -1.710 -1.600 -1.438 0.181 -1.715 -1.580 -1.382 0.180 -1.729 -1.570 -1.336 0.177 -1.705 -1.522 -1.251 0.182 -1.688 -1.480 -1.173 0.185 -1.682 -1.450 -1.107 0.186 -1.660 -1.403 -1.024 0.190 (a) Discuss how you would use this information to choose two candidate VARs for modeling these series. (b) The table below presents the results of performing Breusch-Godrey auxiliary VAR regression tests for serial correlation on each of these 10 VARs. P 1 2 3 4 5 6 7 8 9 10 Test Statistic 92.149 53.851 33.487 34.625 30-746 17.062 14-246 14.713 16.610 20-527 p-value Test DoF 0 0.00001 0.006 0.004 0-014 0.382 0-580 0.546 0.411 0.197 16 16 16 16 16 16 16 16 16 16 (i) State the null and alternative hypotheses for the test being performed. (ii) Discuss whether or not this information is useful in choosing between the two VARS suggested by (a). (c) A colleague of the researcher suggests the individual series need to be tested for non-stationarity. How would you do this using the ADF test? 5. A researcher is investigating the realtionship between US GDP and Consumption growth. The data, which has been collected quarterly and is from 1960 to 2019, is plotted below: GR US CU and Consumption Growth Hataw 1960 to 2015 1970 1800 1200 2000 Conaryton 2010 2000 The researcher has decided to fit VAR(P) models to this bivariate system and has obtained Information Criteria measures for P=1 to 10. These are presented in the table below: P 1 2 3 4 5 6 7 8 9 10 AIC(P) HQ(P) SC(P) FPE(P) -1.429 -1.393 -1.339 0.239 -1.604 -1.543 -1.453 0.201 -1.720 -1.635 -1.509 0.179 -1.710 -1.600 -1.438 0.181 -1.715 -1.580 -1.382 0.180 -1.729 -1.570 -1.336 0.177 -1.705 -1.522 -1.251 0.182 -1.688 -1.480 -1.173 0.185 -1.682 -1.450 -1.107 0.186 -1.660 -1.403 -1.024 0.190 (a) Discuss how you would use this information to choose two candidate VARs for modeling these series. (b) The table below presents the results of performing Breusch-Godrey auxiliary VAR regression tests for serial correlation on each of these 10 VARs. P 1 2 3 4 5 6 7 8 9 10 Test Statistic 92.149 53.851 33.487 34.625 30-746 17.062 14-246 14.713 16.610 20-527 p-value Test DoF 0 0.00001 0.006 0.004 0-014 0.382 0-580 0.546 0.411 0.197 16 16 16 16 16 16 16 16 16 16 (i) State the null and alternative hypotheses for the test being performed. (ii) Discuss whether or not this information is useful in choosing between the two VARS suggested by (a). (c) A colleague of the researcher suggests the individual series need to be tested for non-stationarity. How would you do this using the ADF test?