a) Simulate a time series of length 1000 for the following model, giving appropriate R code and placing the simulated data in a vector x:
b) Plot the correlogram and partial correlogram for the simulated data. Comment on the plots.
c) Fit an AR model to the data in x giving the parameter estimates and order of the fitted AR process.
d) Construct 95% confidence intervals for the parameter estimates of the fitted model. Do the model parameters fall within the confidence intervals? Explain your results.
e) Is the model in Equation (4.25) stationary or non-stationary? Justify your answer.
f) Plot the correlogram of the residuals of the fitted model, and comment on the plot.
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