The following two plots show exponentially weighted moving averages of the percentage change in the US gross national product (GNP). The time seriesis quarterly, from 1960 through the first quarter of 2012. The first graph shows the EWMA with w = 0.5, whereas on the second shows w = 0.9. The EWMA in both cases is shown as a red line with the surrounding data. (The Federal Reserve Bank of St. Louis provides these data online.)
(a) Which weight w do you think produces a better summary of the underlying trend in the percentage changes in GNP? Explain your choice.
(b) Which EWMA would you prefer to use to fore-cast the next value of this series (second quarter of 2012)?

(c) How accurate would you expect your forecast for GNP to be? From looking at these plots, suggest a range.

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