V (20 points) Consider the following time series data. week 1 2 3 4 5 6 value 8

Question

V (20 points) Consider the following time series data. week 1 2 3 4 5 6 value 8 13 15 17 16 9 a. Develop a three-week moving average for this time series and compute the MSE for the three-week moving average.(5 points) b. Use =0.4 to compute the exponential smoothing values for the time series and compute MSE. (5 points) c. Using a weight of 1/2 for the most recent observation, 1/3 for the second most recent, and 1/6 for third most recent, compute a three-week weighted moving average for the time series and compute MSE. (5 points) d. Which appears to provide the best forecast? why?(2 points) e. What is the forecast for week7?(3 points)

Explanation / Answer

a. THree week moving average is sum of demand for last three months

Here

MSE = 1/3 *(25 + 1 + 49) = 25

(b) Here alpha a = 0.4

yt = 0.4 yt-1 + 0.6 Ft-1

MSE = 1/5 * (25 + 25 + 25 + 4 + 33.64) =  22.528

(c) Now weighted average

Ft = 1/2 Ft-1  + 1/3 Ft-2 + 1/6 Ft-3

MSE = 1/3 * (14.69 + 0.11 + 51.36) = 22.0533

(d) Here weighted mean average provides the best forecast because it has lowest MSE

(e) SO forecast for week 7 acocrding to this method is

F7 = 1/2 * F6 + 1/3 * F5 + 1/6 * F4 = 1/2 * 9+ 1/3 * 16 + 1/6 * 17 = 12.67

Week Value Forecast (3MA) Error (Y - F) (Y - F)^2 1 8 2 13 3 15 4 17 12 5 25 5 16 15 1 1 6 9 16 -7 49

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