Circuit City Inc. is a retailer of video and audio equipment and other consumer electronics and office products. Recently, sales have been weak, declining by a total of 5% in December. Among the reasons were a fiercely competitive retailing environment among consumer-electronics sellers, price deflation in many products, a slump in store traffic, and sluggish demand for most computer hardware items. Jim Lowe has the task of forecasting sales for 2003. Jim has access to estimates provided by The Value Line Investment Survey (see Table P-19); however, he is afraid that they are optimistic.

a. Plot the data from 1996 through 2002 as a time series. Do these data appear to be seasonal? Calculate the autocorrelation function.
b. From the results in part a, an autoregressive model with the predictor variable sales lagged four time periods might be appropriate. Why?
c. Let Yt be Circuit City sales. Using the data through 2002, fit an autoregressive model of the form Yt = β0 + β1Yt-4 + εt, and store the residuals. Compute the residual autocorrelations.
d. Use the fitted model from part c to generate forecasts of sales for the four quarters of 2003. Compare your forecasts with the Value Line estimates.
e. Was Jim correct to think the Value Line estimates for 2003 were optimistic?
f. Do you think the autoregressive model in part c can be improved? Discuss.

TABLE P-19 Year May 31 Aug 31 Nov 30 Feb 28 1996 1997 1998 1999 2000 2001 2002 2003 1,742 1,851 2,078 2,205 2.449 1,882 2,118 2,150 1.806 1,948 2,369 2.423 2.566 2,037 2.221 2,350 1.,999 2,039 2,222 2,495 2,336 2.2 2,897 3.156 3.289 3,476 3,137 3,391 3.239 3,400 2,422 2,600