Suppose the monthly sales for a particular product for the past 20 months have b

Question

Suppose the monthly sales for a particular product for the past 20 months have been as follows: a. Use a five-period moving average to compute forecasts of sales for months 6 to 20 and a seven-period moving average to compute forecasts for months 8 to 20. Which fits the data better for months 8 to 20? Explain. b. Use an exponential smoothing approach with smoothing constant alpha = 0.2 to forecast sales for months 2 to 20. Change alpha to 0.1. Does this make the fit better or worse? Explain. c. Use an exponential smoothing with a linear trend and smoothing constants alpha = 0.4 and beta = 0.2 to predict output for months 2 to 20. Does this fit better or worse than your answers to b? Explain.

Explanation / Answer

Forecast equation : Yt = lt + h *bt

where , h= 1

Level eq. : lt =alpha * yt + (1-alpha) * (l(t-1)+b(t-1))

Where l(t-1) = l0 = y1

b(t-1) = b0= y2-y1

Trend eq. : bt=beta * (lt + l(t-1)) + (1-beta) * b(t-1)

alpha = 0.4 , beta= 0.2

Month Sales lt bt yt 1 22 22 -1 2 21 22.2 -0.76 23.2 3 24 23.376 -0.3728 24.376 4 30 26.24928 0.276416 27.24928 5 25 25.58372 0.08802 26.58372 6 25 25.29742 0.013156 26.29742 7 33 28.37056 0.625153 29.37056 8 50 36.64724 2.155459 37.64724 9 36 35.09507 1.413933 36.09507 10 39 35.80868 1.273869 36.80868 11 50 40.72089 2.001536 41.72089 12 55 45.23161 2.503374 46.23161 13 44 43.23694 1.603765 44.23694 14 48 44.17991 1.471605 45.17991 15 55 47.62498 1.866299 48.62498 16 47 46.25521 1.219085 47.25521 17 61 51.42167 2.008561 52.42167 18 58 52.84787 1.892087 53.84787 19 55 52.57347 1.45879 53.57347 20 60 54.66881 1.5861 55.66881 31.84962 -3.29496 32.84962

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