Question

Consider the following time series data.

Week	1	2	3	4	5	6
Value	19	14	17	12	18	14

a. Which of the following is a correct time series plot for this data?

Plot 1

Plot 2

Plot 3

What type of pattern exists in the data?

Vertical

Horizontal

Scatter

b. Develop the three-week moving average forecasts for this time series. Compute MSE and a forecast for week 7 (to 2 decimals if necessary).

MSE
The forecast for week 7

c. Use alpha = 0.02 to compute the exponential smoothing forecasts for the time series. Compute MSE and a forecast for week 7 (to 2 decimals).

MSE
The forecast for week 7

d. Compare the three-week moving average approach with the exponential smoothing approach using alpha = 0.02. Which appears to provide more accurate forecasts based on MSE?
The three-week moving average provides a better forecast since it has a smaller MSE

The exponential smoothing approach provides a better forecast since it has a smaller MSE

The three-week moving average provides a better forecast since it has a larger MSE

e. Use a smoothing constant of alpha = 0.04 to compute the MSE (to 2 decimals).

Does a smoothing constant of 0.02 or 0.04 appear to provide more accurate forecasts based on MSE?

The exponential smoothing forecast using alpha = 0.04 provides a worse/better forecast than the exponential smoothing forecast using alpha = 0.02 since it has a smaller MSE

Answer 1

a)

plot 1

HorizontaL

B)

Time period	Actual Value(A)	Moving avg. Forecast(F)	Forecast error E=|A-F|	Squared Forecast Error
1	19
2	14
3	17
4	12	16.67	4.67	21.78
5	18	14.33	3.67	13.44
6	14	15.67	1.67	2.78
		Total	10.00	38.00
		Average	3.33	12.67
			MAD	MSE
MSE =			12.67
forecast for week 7 =	14.67

C)

Time period	Actual Value(A)	Forecast(F)	Forecast error E=A-F	Squared Forecast Error
1	19
2	14	19.00	5.00	25.00
3	17	18.00	1.00	1.00
4	12	17.80	5.80	33.64
5	18	16.64	1.36	1.85
6	14	16.91	2.91	8.48
		Total	16.07	69.97
		Average	3.21	13.99
			MAD	MSE
MSE =			13.99
forecast for week 7 =	16.33

d)

The three-month moving average provides a better forecast since it has a smaller MSE

e)

MSE =12.77

0.4 provides a better forecast