Question

Problem 15-05 (Algorithmic)

Consider the following time series data.

Week	1	2	3	4	5	6
Value	16	13	18	11	15	14

1. Develop a three-week moving average for this time series. Compute MSE and a forecast for week 7. Round your answers to two decimal places.

   Week	Time Series Value	Forecast
   1	16
   2	13
   3	18
   4	11
   5	15
   6	14

   
   MSE: ——————
   
   The forecast for week 7: ————————
   
2. Use  = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7. Round your answers to two decimal places.

   Week	Time Series Value	Forecast
   1	16
   2	13
   3	18
   4	11
   5	15
   6	14

   
   MSE: ————————
   
   The forecast for week 7: ——————
3. Use trial and error to find a value of the exponential smoothing coefficient  that results in a smaller MSE than what you calculated for  = 0.2. Find a value of  for the smallest MSE. Round your answer to three decimal places.
   
   alpha = ——————————

Answer 1

a)

Ft= forecast for period t,

At= actual demand in period t,

Et= forecast error in period t.

The 3-period moving average forecast for period t, Ft=(At−1+At−2+At−3)/3

**week 4 would be  the 1st week to generate a 3-week moving average forecast

**Forecast for week 7 would be (A4+A5+A6)/3

**MSE (Mean Squared Error) = =(E4^2+E5^2+E6^2)/3

WEEK	TIME SERIES VALUE (At)	3 WEEK MOVING AVG (Ft)	Et=At- Ft
1	16
2	13
3	18
4	11	15.66666667	-4.66667
5	15	14	1
6	14	14.66666667	-0.66667
7	F7 (forecast for week 7)	13.33333333
	MSE (Mean Squared Error)	7.740740741

b)

WEEK	TIME SERIES VALUE (At)	Forecasting(Using exponetial a=0.2)	Lt	SSE
0			14.5
1	16	14.5	14.8	0.09
2	13	14.8	14.44	0.1296
3	18	14.44	15.152	0.506944
4	11	15.152	14.3216	0.689564
5	15	14.3216	14.45728	0.018409
6	14	14.45728	14.365824	0.008364
7	F7	14.365824	SSE	1.442881
SSE	sum of (at-forecasting)^2	1.442881422
MSE	SSE/(t-1)	0.240480237
F7		14.365824

Mean (L0)	14.5
Alpha	0.2
Mean (L0)	14.5
L1	ay1 + (1-a)L0

Formula for forecasting

L1	ay1 + (1-a)L0