Question

Consider the following time series data. Week 1 2 3 4 5 6 Value 19 11 16 1017 15 (a) Construct a time series plot. 20 20 20 18 16 14 12 10 c 14 12 12 0 23 4 5 67 0 23 4 5 67 Week Weck Week 20 18 0 1 2345 6 7 Week What type of pattern exists in the data? The data appear to follow a seasonal pattern. The data appear to follow a cyclical pattern. O The data appear to follow a trend pattern 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 Forecast Value 19 16 10 17 15 Compute MSE. (Round your answer to two decimal places) MSE What is the forecast for week 7? (c) Use α-0.2 to compute the exponential smoothing forecasts for the time series. Time Series Value Week Forecast 19 її 16 10 17 15 Compute MSE. (Round your answer to two decimal places.) MSE What is the forecast for week 7? (Round your answer to two decimal places.) d) Compare the three-week moving average approach with the exponential smoothing approach using α·O 2 hich appears to provide more accurate recasts based on MSE? Ex pain. The three-week moving average provides a better forecast since it has a smaller MSE than the smoothing approach The exponential smoothing using a-0.2 provides a better forecast since it has a larger MSE than the three-week moving average approach. The three-week moving average provides a better forecast since it has a larger MSE than the smoothing approach. O The exponential smoothing using α = 0.2 provides a better forecast since it has a smaller MSE than the three-week moving average approach. (e) Use a smoothing constant of α 0.4 to compute the exponential smoothing forecasts. Time SeriesForecast Week Value 10 17 15 Does a smoothing constant of 0.2 or 0.4 appear to provide more accurate forecasts based on MSE? Expn The exponential smoothing using α = 0.2 provides a better forecast since it has a larger MSE than the exponential smoothing using α-0.4 The exponential smoothing using α = 0.4 provides a better forecast since it has a larger MSE than the exponential smoothing using α-0.2 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 The exponential smoothing using α = 0.2 provides a better forecast since it has a smaller MSE than the exponential smoothing using α = 0.4

Answer 1

a) bottom one plot is correct

cyclical

b)

Time period	Actual Value(A)	Moving avg. Forecast(F)	Forecast error E=|A-F|	Squared Forecast Error
1	19
2	11
3	16
4	10	15.33	5.33	28.44
5	17	12.33	4.67	21.78
6	15	14.33	0.67	0.44
		Total	10.67	50.67
		Average	3.56	16.89
			MAD	MSE

MSE=16.89

forecast =14

c)

Time period	Actual Value(A)	Forecast(F)	Forecast error E=A-F	Squared Forecast Error
1	19
2	11	19.00	8.00	64.00
3	16	17.40	1.40	1.96
4	10	17.12	7.12	50.69
5	17	15.70	1.30	1.70
6	15	15.96	0.96	0.92
		Total	18.78	119.27
		Average	3.76	23.85
			MAD	MSE

MSE=23.85

forecast =15.77

d)

three week moving average is better..smaller MSE

e)

Time period	Actual Value(A)	Forecast(F)
1	19
2	11	19.00
3	16	15.80
4	10	15.88
5	17	13.53
6	15	14.92

using alpha =0.4 provide better ..smaller MSE