Question 2 [30 marks] The time plot below shows monthly values for the Index of Industrial Production in Japan, from Jan 1995 to Dec 2006. 110 105 iip 100 / Wh mwy wyzna 95 1996m01 1998m01 2000m01 2002m01 2004m01 2006m01 date A researcher runs the following regressions on D.iipt = (iipt iipt-1): D. iipt = iipt-1 + e{?? D. iipt = a + iipt-1 + e{2), D. iipt = a + iipt-1+ y trend + e(3), using data from Jan 1978 to Dec 2006 (so longer than shown in the graph above). The superscripts on the error terms are there to indicate that the residuals between the three models are different from each other. a) What are the above regressions testing? What are the null and alternative hypotheses? What is the reason behind the different regression models? Which one would be most appropriate given the graph above? Explain. [10 marks] b) The relevant statistics from the three models above are -1.907, -1.760 and -2.021. What do you conclude regarding the stationarity of the time series? [10 marks] c) The researcher estimates the following models from the third model in part (a): D. iipt = a + B iipt-1 + y trend + D. iipt-1 + 4), D. iipt = a + b iipt-1 + y trend + 04 D. iipt-1 + 02D. iipt-2 +ex5). Explain the purpose of this change. How can the Breusch-Godfrey test help identify the number of regressors added to the model? [10 marks] Question 2 [30 marks] The time plot below shows monthly values for the Index of Industrial Production in Japan, from Jan 1995 to Dec 2006. 110 105 iip 100 / Wh mwy wyzna 95 1996m01 1998m01 2000m01 2002m01 2004m01 2006m01 date A researcher runs the following regressions on D.iipt = (iipt iipt-1): D. iipt = iipt-1 + e{?? D. iipt = a + iipt-1 + e{2), D. iipt = a + iipt-1+ y trend + e(3), using data from Jan 1978 to Dec 2006 (so longer than shown in the graph above). The superscripts on the error terms are there to indicate that the residuals between the three models are different from each other. a) What are the above regressions testing? What are the null and alternative hypotheses? What is the reason behind the different regression models? Which one would be most appropriate given the graph above? Explain. [10 marks] b) The relevant statistics from the three models above are -1.907, -1.760 and -2.021. What do you conclude regarding the stationarity of the time series? [10 marks] c) The researcher estimates the following models from the third model in part (a): D. iipt = a + B iipt-1 + y trend + D. iipt-1 + 4), D. iipt = a + b iipt-1 + y trend + 04 D. iipt-1 + 02D. iipt-2 +ex5). Explain the purpose of this change. How can the Breusch-Godfrey test help identify the number of regressors added to the model? [10 marks]
