# solution

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Exponential smoothing models are so named because the coefficients

w, (1 âˆ’ w)w, (1 âˆ’ w)2w, . . . , (1 âˆ’ w)nâˆ’2w

decrease in value exponentially. For this exercise, take n = 11. Use software to do the calculations.

(a) Calculate the coefficients for a smoothing constant ofw =0.1.

(b) Calculate the coefficients for a smoothing constant ofw =0.5.

(c) Calculate the coefficients for a smoothing constant ofw =0.9.

(d) Plot each set of coefficients from parts (a), (b), and (c).

The coefficient values should be measured on the vertical axis while the horizontal axis can simply be numbered 1, 2, . . . , 9, 10 for the 10 coefficients from each part. Be sure to use a different plotting symbol and/or color to distinguish the three sets of coefficients and connect the points for each set. Also, label the plot so that it is clear which curve corresponds to each value of w used.

(e) Describe each curve in part (d). Which curve puts more weight on the most recent value of the time series when calculating a

forecast?

(f) The coefficient of y1 in the exponential smoothing model is (1âˆ’w)nâˆ’1. Calculate the coefficient of y1 for each of the values of w in parts (a), (b), and (c). How do these values compare to the first 10 coefficients you calculated for each value of w? Which value of w puts the greatest weight on y1 when calculating a forecast?

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