Consider the following time series data Week 1 2 3 4 5 6 Val

Consider the following time series data.

Week 1 2 3 4 5 6

Value 18 13 16 11 17 14

A. Construct a time series plot. What type of pattern exists in the data?

B. Develop a three-week moving average for this time series. Compute MSE and forecast for week 7.

C. use a=0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7.

D. Compare the three-week moving average forecast with the exponential smoothing forecast using a=02. Which appears to provide the better forecast based on MSE? Explain.

Solution

The data appear to follow a horizontal pattern.

b)

1   18          
2   13          
3   16          
4   11   15.67   -4.67   21.78
5   17   13.33   3.67   13.44
6   14   14.67   -0.67       0.44
           Total   35.67

       MSE = 35.67/3 = 11.89.

The forecast for week 7 = (11 + 17 + 14) / 3 = 14

c)

Smoothing constant = .2
Week TSV    Forecast   Forecast Error   Squared Forecast
1   18          
2   13   18.00   -5.00   25.00
3   16   17.00   -1.00   1.00
4   11   16.80   -5.80   33.64
5   17   15.64   1.36   1.85
6   14   15.91   -1.91      3.66
           Total   65.15

       MSE = 65.15/5 = 13.03

The forecast for week 7 is .2(14) + (1 - .2)15.91 = 15.53

D) The three-week moving average provides a better forecast since it has a smaller MSE.