Simulate an AR(2) model with n = 48, φ1 = 1.5, and φ2 = −0.75. (a) Fit the correctly specified AR(2) model and look at a time series plot of the residuals. Does the plot support the AR(2) specification? (b)Display a normal quantile-quantile plot of the standardized residuals. Does the plot support the AR(2) specification? (c) Display the sample ACF of the residuals. Does the plot support the AR(2) specification? (d)Calculate the Ljung-Box statistic summing to K = 12. Does this statistic support the AR(2) specification?