The 2024 June quarter CPI will be released by the ABS on the 31st of July. In this assignment, you will use the most recently published data to forecast the growth in the CPI from the March quarter to the June quarter. This Gretl data set includes data on the quarter-by-quarter CPI inflation rate from the March quarter of 1978 to the March quarter of 2024 (the latest quarterly figure available).

1. (2 marks) Plot the CPI inflation rate and comment on its time series behaviour. Does it look stationary? Would you expect it to be stationary?

2. (3 marks) Estimate an autoregression for the level of the CPI inflation rate. You should estimate the order of the autoregression using the AIC and a maximum possible lag of 6 quarters. In your answer, you should provide a table that contains each order considered and the corresponding value of the AIC. You should place an asterisk next to the smallest value of the AIC.

3. (2 marks) Does your autoregression have a heteroscedasticity problem? How do you know? If it does, propose and implement a remedy propose and implement a remedy.

4. (2 marks) Test the null hypothesis that your autoregression does not have autocorrelation against the alternative hypothesis that it has sixth-order autocorrelation. What do you conclude? If you find evidence of autocorrelation, propose and implement a remedy.

5. (3 marks) Use your estimated autoregression to forecast the June Quarter 2024 CPI inflation rate. Also, compute an 80% forecast interval for the June Quarter CPI Inflation rate.

6. (2 marks) Test the null hypothesis that the autoregression does not have any structural breaks over the time span covered by the sample. Use the critical value method with a 5% significance level. If you find evidence of a structural break, when do you estimate that it occurs?

7. (5 marks) Adjust the sample so that it includes data only from the first quarter of 1992 to the first quarter of 2024. Repeat your analysis from questions 2 to 6 with this smaller data set.

8. (2 marks) Is your forecast interval computed in Question 7 narrower or wider than the forecast interval that you computed in Question 5? Why do you think that this is the case?