Question

Use the following time-series data to answer the given questions. Time Period Value 1 27 2 30 3 58 4 63 5 59 6 67 7 70 8 86 9 101 10 97 a. Develop forecasts for periods 5 through 10 using 4-month moving averages. b. Develop forecasts for periods 5 through 10 using 4-month weighted moving averages. Weight the most recent month by a factor of 4, the previous month by 2, and the other months by 1. c. Compute the errors of the forecasts in parts (a) and (b) and observe the differences in the errors forecast by the two different techniques. (Round your answers to 3 decimal places.) a. Time Period Value 4-Month Moving Average Forecast 1 27 - 2 30 - 3 58 - 4 63 - 5 59 6 67 7 70 8 86 9 101 10 97 b. Time Period Value 4-Month Weighted Moving Average Forecast 1 27 - 2 30 - 3 58 - 4 63 - 5 59 6 67 7 70 8 86 9 101 10 97 c. Time Period Value Forecast Error, 4-Month Moving Average Forecast Error, 4-Month Weighted Moving Average Differences in error 1 27 - - - 2 30 - - - 3 58 - - - 4 63 - - - 5 59 6 67 7 70 8 86 9 101 10 97 In each time period, the four-month moving average produces errors of forecast than the four-month weighted moving average.

Answer 1

Time Period	Value	4 Month MA	4 Month WMA	Error 4 MMA	Error 4MWMA	Differnce in Error_1	Difference in Error_2
1	27
2	30
3	58
4	63
5	59	45.25	54	13.75	5	8.75	0.636363636
6	67	53.5	56.875	12.5	9.125	3.375	0.27
7	70	62	63.125	8	6.875	1.125	0.140625
8	86	64.75	66.875	21.25	19.125	2.125	0.1
9	101	70.25	76.125	30.75	24.875	5.875	0.191056911
10	97	80.75	89	16.25	8	8.25	0.507692308
4 month Moving Average at time (i)=(value(i-1)+value(i-2)+value(i-3)+value(i-4))/4
4 Month Weighted moving avergae at time(i)=(4*value(i-1)+2*value(i-2)+value(i-3)+value(i-4))/8
Error 4 MMA at time(i)=value(i)-4 Month MA(i)
Error 4 MWMA at time(i)=value(i)-4 Month WMA(i)
Differnce in Error_1=Error 4MMA(i)-Error 4MWMA(i)
Differnce in Error_2=(4MMA(i)-Error 4MWMA(i))/Error 4MMA(i)
We can easily see that Weighted Moving average Yield less error