Problem 15-05 (Algorithmic) Consider the following time series data. Week 1 2 3 4 5 6 Value 16 13 18 11 15 14 Develop a three-week moving average for this time...

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Finance

Problem 15-05 (Algorithmic)
Consider the following time series data.
Week 1 2 3 4 5 6
Value 16 13 18 11 15 14

Develop a three-week moving average for this time series.Compute MSE and a forecast for week 7. Round your answers to twodecimal places.
Week Time Series
Value Forecast
1 16
2 13
3 18
4 11
5 15
6 14

MSE: ——————

The forecast for week 7: ————————
Use = 0.2 to compute the exponential smoothingvalues 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: ——————
Use trial and error to find a value of the exponentialsmoothing coefficient that results in a smaller MSE thanwhat you calculated for = 0.2. Find a valueof for the smallest MSE. Round your answer to threedecimal places.

alpha = ——————————

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

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

Answer & Explanation Solved by verified expert

3.9 Ratings (694 Votes)

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

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

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Transcribed Image Text

Problem 15-05 (Algorithmic)Consider the following time series data.Week123456Value161318111514Develop a three-week moving average for this time series.Compute MSE and a forecast for week 7. Round your answers to twodecimal places.WeekTime SeriesValueForecast116213318411515614MSE: ——————The forecast for week 7: ————————Use = 0.2 to compute the exponential smoothingvalues for the time series. Compute MSE and a forecast for week 7.Round your answers to two decimal places.WeekTime SeriesValueForecast116213318411515614MSE: ————————The forecast for week 7: ——————Use trial and error to find a value of the exponentialsmoothing coefficient that results in a smaller MSE thanwhat you calculated for = 0.2. Find a valueof for the smallest MSE. Round your answer to threedecimal places.alpha = ——————————

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