EWMA time series question with plots and i have no idea what to do

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Question description

01020-303QuarterPercent Change

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x y graph


The plots to the left and right show exponentially weighted moving averages​ (EWMA) of the percentage change of a​ country's gross national product​ (GNP). The time series is quarterly for a​ five-year period. To the​ left, the weight w in the EWMA is




to the right. The EWMA in both cases is shown as a line and the surrounding data as dots. Complete parts a through c below.

01020-303QuarterPercent Change

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x y graph


(a) Which smoothing constant do you think produces a better summary of the underlying trend in the percentage changes in​ GNP?

The EWMA with



is better because it

captures less random variation.

(b) In the most recent quarter​ (the last data point in this​ series), the GNP was estimated to be



What would you​ forecast, having seen these​ plots, for GNP for the next​ quarter?

The GNP for the next quarter should be about



(Round to three decimal places as​ needed.)

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