Suppose an autoregressive model is used for data in which quarterly sales in 2017 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 2018.

b) Compare this forecast with the actual value ($2.9 billion) 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 four, use the following model to compute a forecast for Q₁ of 2018: y_t = 0.410 + 1.35y_t - 4. Compare the APE for this forecast to that in (a). Compare the appropriateness of the different models.