Q2. Consider the second order autoregressive model Yt = 1.0+ 1.8yt-1 − 0.81yt-2 + et where et is described in Q1(a). In

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Q2 Consider The Second Order Autoregressive Model Yt 1 0 1 8yt 1 0 81yt 2 Et Where Et Is Described In Q1 A In 1 (173.34 KiB) Viewed 30 times

Q2. Consider the second order autoregressive model Yt = 1.0+ 1.8yt-1 − 0.81yt-2 + et where et is described in Q1(a). In this problem use the numeric part of your zid to set the random number seed in set.seed (zid). Please generate 162 observations from this model, taking y₁ = y2 = 4. For the rest of the question, please just use the last 140 values of the yt, i.e., Y23,,Y162. (a) Is this autoregressive model stationary? Justify your answer. (b) Estimate the mean and variance of yt from your generated data. Estimate the first five autocorrelations of the yt from the data. (d) Please now pretend that you do not know how the model was generated. Please fit a first order autoregressive model to the Y23,, Y122 and report your results. (e) Please carry out time series cross validation on the fitted model and report the resulting RMSE and MAE for the predictions. Use observations y123,..., 162 for this. (f) Please carry out the following diagnostics for the fitted model: plot yt vs fitted and standardized residuals vs fitted; normal quantile plot of the standardized residuals. Report the results. (g) Carry out a Ljung-Box test on the residuals and report the result. (h) Report the AICC and BIC scores for your model based on the training data, i.e., observations Y23,..., 122. (i) From the above, what do you conclude about the fit of an AR(1) model to the data ?