Construct time series and ACF plots of the parameters phi and sigma. (a) Do you believe that the MCMC sample size is adequate? Why or why not? Is the burn-in iterations adequate? Why or why not? If...

Construct time series and ACF plots of the parameters phi and sigma.

(a) Do you believe that the MCMC sample size is adequate? Why or why not? Is the burn-in iterations adequate? Why or why not? If you feel that either the number of iterations or the length of the burn-in period is inadequate, then rerun with a larger burn-in period and/or MCMC sample size.

(b) Compute the MLEs for this model using arima(). How closely do the Bayes estimates and MLEs agree? Could you explain any possible disagreement?

(c) The model in the BUGS program does not assume that the time series is in its stationary distribution. In fact, the model does not even assume that there is a stationary distribution. Explain why.

(d) Modify the BUGS program to utilize the marginal distribution of y1, assuming that the process starts in its stationary distribution.