Problem
a. Estimate an AR(1) model for ?Yt. What is the estimated AR(1) coefficient? Is the coefficient statistically significantly different from zero? Construct a 95% confidence interval for the population AR(1) coefficient.
b. Estimate an AR(2) model for ?Yt. Is the AR(2) coefficient statistically significantly different from zero? Is this model preferred to the AR(1) model?
c. Estimate AR(3) and AR(4) models. (i) Using the estimated AR(1) through AR(4) models, use BIC to choose the number of lags in the AR model. (ii) How many lags does AIC choose?
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.