Suppose an autoregressive model is used for data in which quarterly sales in 2013 were: 1.9, 1.7, 2.2, and 2.3 ($ Billion).
a) If a first-order autoregressive model is developed with estimated parameters of b0 = 0.100 and b1 = 1.12, compute the forecast for Q1 of 2014.
b) Compare this forecast to the actual value ($ 2.9B) by computing the absolute percentage error (APE). Did you over-forecast or under- forecast?
c) Assuming these quarterly sales have a seasonal component of length 4, use the following model to compute a forecast for Q4 of 2014: yt = 0.410 + 1.35 yt - 4. In fact, Q4 sales were $ 3.4B. Compare the APE for this forecast to that in part a. Compare the appropriateness of the different models.