Question

Consider the following time series data.

Week	1	2	3	4	5	6
Value	18	12	16	10	17	15

(a) Construct a time series plot.

What type of pattern exists in the data? The data appear to follow a horizontal pattern.

(b) Develop the three-week moving average forecasts for this time series. (Round your answers to two decimal places.)

Week	Time Series Value	Forecast
1	18
2	12
3	16
4	10	15.33
5	17	12.67
6	15	14.33

Compute MSE. (Round your answer to two decimal places.)

MSE = 15.89

What is the forecast for week 7? 14.00

(c) Use α = 0.2 to compute the exponential smoothing forecasts for the time series.

Week	Time Series Value	Forecast
1	18
2	12	18
3	16	16.80
4	10	16.64
5	17
6	15

Compute MSE. (Round your answer to two decimal places.)

MSE = 16.80

What is the forecast for week 7? (Round your answer to two decimal places.) 15.52

(d) Compare the three-week moving average approach with the exponential smoothing approach using  α = 0.2.  Which appears to provide more accurate forecasts based on MSE? Explain.

The three-week moving average provides a better forecast since it has a smaller MSE than the smoothing approach.

(e) Use a smoothing constant of α = 0.4 to compute the exponential smoothing forecasts.

Week	Time Series Value	Forecast
1	18
2	12	18
3	16	15.60
4	10	15.76
5	17
6	15

Does a smoothing constant of 0.2 or 0.4 appear to provide more accurate forecasts based on MSE? Explain. .The exponential smoothing using α = 0.4 provides a better forecast since it has a smaller MSE than the exponential smoothing using α = 0.2.

Missing 5 and 6 from both charts

Answer 1

a)

horizontal pattern

Time period	Actual Value(A)	Moving avg. Forecast(F)	Forecast error E=|A-F|
1	18
2	12
3	16
4	10	15.33	5.33
5	17	12.67	4.33
6	15	14.33	0.67
		Total	10.33
		Average	3.44
			MAD
MSE =			15.89
forecast for week 7 =			14.00

c)

Time period	Actual Value(A)	Forecast(F)	Forecast error E=A-F	Squared Forecast Error
1	18
2	12	18.00	6.00	36.00
3	16	16.80	0.80	0.64
4	10	16.64	6.64	44.09
5	17	15.31	1.69	2.85
6	15	15.65	0.65	0.42
		Total	15.78	84.00
		Average	3.16	16.80
			MAD	MSE
MSE =			16.80
forecast for week 7 =			15.52

d)

The three-week moving average provides a better forecast since it has a smaller MSE than the smoothing approach.

e)

Time period	Actual Value(A)	Forecast(F)	Forecast error E=A-F	Squared Forecast Error
1	18
2	12	18.00	6.00	36.00
3	16	15.60	0.40	0.16
4	10	15.76	5.76	33.18
5	17	13.46	3.54	12.56
6	15	14.87	0.13	0.02
		Total	15.83	81.91
		Average	3.17	16.38
			MAD	MSE
MSE =			16.38

The exponential smoothing using α = 0.4 provides a better forecast since it has a smaller MSE than the exponential smoothing using α = 0.2.