Part C Assume that you have a sample of size N=1,000 generated from the AR(2) model...

Transcribed Image Text:

Part C Assume that you have a sample of size N=1,000 generated from the AR(2) model (2) yt=0.2+0.9 yt-1 + 0.01 yt-2 + t where &~iid(0,0). 1. Given the sample data, explain how you can test if the AR(2) model of Eq. 2 has a unit root or not. Clearly describe the procedure, the variables used, and the test statistic and its hypotheses. I [25 marks] 2. What test result would you expect? Does your expectation change, if you only had a sample of size T=30. [15 marks] 3. Assume that you have fitted an AR(1) model to the data generated by Eq. 1. The estimated model is (3) Jt= = 0.19 +0.92yt-1 Discuss why you might prefer the estimated model of Eq. 3 over estimates of an AR(2) model if you wanted to use the estimated models for forecasting. How does your answer change, if you knew that your data has been generated by Eq. 2? [20 marks] 4. Assume that the observed value of the time-series in period t is given by yt = 1.65 Using equations were appropriate, explain can how you obtain a 1-period ahead forecast y++1 given the estimated model of Eq. 3? What is the forecasted value? [25 marks] 5. How does your answer change, if you wanted to make a h-period ahead forecast with h=2 and, respectively, h=100? [15 marks] 2 Part C Assume that you have a sample of size N=1,000 generated from the AR(2) model (2) yt=0.2+0.9 yt-1 + 0.01 yt-2 + t where &~iid(0,0). 1. Given the sample data, explain how you can test if the AR(2) model of Eq. 2 has a unit root or not. Clearly describe the procedure, the variables used, and the test statistic and its hypotheses. I [25 marks] 2. What test result would you expect? Does your expectation change, if you only had a sample of size T=30. [15 marks] 3. Assume that you have fitted an AR(1) model to the data generated by Eq. 1. The estimated model is (3) Jt= = 0.19 +0.92yt-1 Discuss why you might prefer the estimated model of Eq. 3 over estimates of an AR(2) model if you wanted to use the estimated models for forecasting. How does your answer change, if you knew that your data has been generated by Eq. 2? [20 marks] 4. Assume that the observed value of the time-series in period t is given by yt = 1.65 Using equations were appropriate, explain can how you obtain a 1-period ahead forecast y++1 given the estimated model of Eq. 3? What is the forecasted value? [25 marks] 5. How does your answer change, if you wanted to make a h-period ahead forecast with h=2 and, respectively, h=100? [15 marks] 2