(a). Plot the series against time. Does it look stationary? Why or why not?
(b). Show the plots for the ACF and PACF for this time series. Describe the general features of the ACF and PACFs. Compare the sample ACF and PACF with those of a theoretical AR(2) process. How well do they conform to the actual plots? Are there any anomalies?
(c). Estimate an AR(1) process – with constant – for this series and save the residuals. Show the estimated coefficients for the regression below. In addition, show the Q statistics for the residuals. What is the null hypothesis associated with the Q statistic in this case? Why do they show that the AR(1) model is inadequate for this time series?
(d). If the underlying data generation process was an ARMA(1,1) model, what properties would you expect the ACF and PACF to have? Based on what you saw in (b), do you think an ARMA(1,1) model is an appropriate candidate? Why or why not?
(e). Now, estimate both an ARMA(1,1) and an AR(2) model and present the results below. Of the three models you have estimated, which is selected by the AIC and SBC criteria? What do the Q statistics suggest about model adequacy for the three models?