Question

Consider the following gasoline sales time series data. Click on the datafile logo to reference the data.

Week	Sales (1000s of gallons)
1	16
2	20
3	19
4	23
5	19
6	15
7	19
8	17
9	23
10	20
11	15
12	21

a. Using a weight of (1/2) for the most recent observation, (1/3) for the second most recent observation, and (1/6) third the most recent observation, compute a three-week weighted moving average for the time series (to 2 decimals). Enter negative values as negative numbers.

a. Using a weight of  for the most recent observation,  for the second most recent observation, and  third the most recent observation, compute a three-week weighted moving average for the time series (to 2 decimals). Enter negative values as negative numbers.

Week	Time-Series Value	Weighted Moving Average Forecast	Forecast Error			(Error)2
1
2
3
4
5
6
7
8
9
10
11
12
-	-	-	-	-	Total

b. Compute the MSE for the weighted moving average in part (a).
MSE =

Answer 1

(a) Here first we will use weighted moving avergae where

so forecast for a given month

F_t+1 = 1/2 y_t + 1/3 y_t-1 + 1/6 y_t-2

Week	Sales	Forecast	Error	Error^2
1	16
2	20
3	19
4	23	18.83	4.167	17.36111
5	19	21.17	2.167	4.694444
6	15	20.33	5.333	28.44444
7	19	17.67	1.333	1.777778
8	17	17.67	0.667	0.444444
9	23	17.33	5.667	32.11111
10	20	20.33	0.333	0.111111
11	15	20.50	5.500	30.25
12	21	18.00	3.000	9
			Total	124.1944

Here MSE = Total/9 = 124.1944/9 = 13.80