Question

omework Consider the following time series data Month 1 2 3 4 5 6 7 Value 21 14 18 13 18 21 14 a. Which of the following is a correct time series plot for this data? や" -Select your answer- What type of pattern exists in the data? -select your answer- b. Develop the three-month moving average forecasts for this time series. Compute MSE and a forecast for month 8 (to 2 decimals if necessary). Enter negative values as negative number. Squared Forecast Forecast Time Series Month Value Forecast Error Error 2 14 3 18 4 13 5 18 6 21 7 14 Totals MSE The forecast for month 8 C. Use α-.2 to compute the exponential smoothing forecasts for the time series. Compute MSE and a forecast for month 8 (to 2 decimals). Enter negative values as negative number Time Squared Forecast Forecast Series Month Value Forecast Error Error 1 21 2 14 3 18 2 to compute the exponential smoothing forecasts for the me series Compute M SE and a forecast or 8 to 2 dec mals Ente negative values as negati e number c. Use α on Time Series Squared Forecast Forecast Month Value Forecast ErrorError 1 21 2 14 3 18 4 13 5 18 6 21 714 Totals MSE The forecast for month 8 d. Compare the three-month moving average approach with he exponential smoothing approach using α- 2. which appears to provide more accurate o ea ts base an M Select your answer e. Use a smoothing constant of α-,4 to compute the MSE. (to 2 decimals) Does a smoothing constant of .2 or .4 appear to provide more accurate forecasts based on MSE? -Select your answer- d. Compare the three-month moving average approach with the exponential smoothing approach using α = .2, which appears to provide more accurate forecasts based on MSE? -Select your answer The three-month 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-month moving average provides a better forecast since it has a larger MSE e. Use a smoothing constant of α-.4 to compute the MSE. (to 2 decimals) Does a smoothing constant of .2 or .4 appear to provide more accurate forecasts based on MSE? -Select your answer - .2 .4

Answer 1

(a) right choice is first.

there is seasonality pattern in the data ( please give the options for appropriate answer)

25 20 15 10

(b)

t	yt	Forecast	forecast error	squared forecast error
1	21
2	14
3	18
4	13	17.6667	-4.6667	21.7778
5	18	15.0000	3.0000	9.0000
6	21	16.3333	4.6667	21.7778
7	14	17.3333	-3.3333	11.1111
			total	63.6667

MSE=SQRT(63.6667/4)=3.9896

forecast for month 8=(18+21+14)/3=17.6667

(c)

	alpha=	0.2
t	Yt	Ft=alpha*Y(t-1)+(1-alpha)*F(t-1)	forecast error	squared forecast error
1	21
2	14	21.0000	-7.0000	49.0000
3	18	19.6000	-1.6000	2.5600
4	13	19.2800	-6.2800	39.4384
5	18	18.0240	-0.0240	0.0006
6	21	18.0192	2.9808	8.8852
7	14	18.6154	-4.6154	21.3015
8		17.6923	total=	121.1857
9			MSE=	4.4942

MSE=sqrt(121.1857/6)=4.4942

forecast for the month 8=17.6923

(d) right choice is first.

since the 3-months moving average MSE is less than exponential smoothing (alpha=0.2 )

(e) alpha=0.4 is better ( than alpha=0.2).

	alpha=	0.4
t	Yt	Ft=alpha*Y(t-1)+(1-alpha)*F(t-1)	forecast error	squared forecast error
1	21
2	14	21.0000	-7.0000	49.0000
3	18	18.2000	-0.2000	0.0400
4	13	18.1200	-5.1200	26.2144
5	18	16.0720	1.9280	3.7172
6	21	16.8432	4.1568	17.2790
7	14	18.5059	-4.5059	20.3033
8		16.7036	total=	116.5539
9			MSE=	4.4075