41 The GNP for each quarter of the past four years is shown in the following table:

YEAR QUARTER GNP (billions)

1 1 $ 9,027 2 $ 9,092 3 $ 9,194 4 $ 9,367 2 1 $ 9,505 2 $ 9,588 3 $ 9,726 4 $ 9,938 3 1 $10,063 2 $10,238 3 $10,285 4 $10,375 4 1 $10,430 2 $10,473 3 $10,501 4 $10,580

(a) Find the optimal value of a that would minimize MAPE for the exponential smoothing model.

(b) What is the linear trend equation that best fits the data? Forecast the GNP for the first quarter of year 5 by using this equation.

(c) Forecast the GNP for the first quarter of year 5 by using a four-period moving average.

(d) Which of these methods is most appropriate to use? Justify your answer.