Given that the mean of the time series in Exercise 9.3 is 50, use the fitted AR(2) model to forecast the future values of the time series x 1 , x 2 , and x 3 ; assuming the current value is x 0 = 76...

Given that the mean of the time series in Exercise 9.3 is 50, use the fitted AR(2) model to forecast the future values of the time series x₁, x₂, and x₃; assuming the current value is x₀
= 76 and the previous value is x_–1
= 65.

Exercise 9.3

Computing sample lag correlations for a time series with n ¼ 100 values, whose variance is 100, yields r₁
= 0.80, r₂
= 0.60, and r₃
= 0.50.

a. Use the Yule-Walker equations to fit AR(1), AR(2), and AR(3) models to the data. Assume the sample size is large enough that Equation 9.26 provides a good estimate for the white noise variance.

b. Select the best autoregressive model for the series according to the BIC statistic.

c. Select the best autoregressive model for the series according to the AIC statistic.