Question

FORECASTING , THE COMPLETE ANSWERS TO THESE QUESTIONS WILL RECEIVE A THUMBS UP!

Weekly demand figures at Hot Pizza are as follows:

Week	Demand
1	108
2	116
3	118
4	124
5	96
6	119
7	96
8	102
9	112
10	102
11	92
12	91

Estimate demand for the next 4 weeks using a 4-week moving average as well as simple exponential smoothing with α = 0.1. Evaluate the MAD, MAPE, MSE, bias, and TS in each case. Which of the two methods do you prefer? Why?

For the Hot Pizza data in Exercise 2, compare the performance of simple exponential smoothing with α = 0.1 and α = 0.9. What difference in forecasts do you observe? Which of the two smoothing constants do you prefer?

I NEED ALL THE ERRORS , FOR MOVING AVERAGE AND EXPONENTIAL SMOOTHING AND THE 4 WEEK FORECAST RESULTS , THANK YOU , THE ANSWERS TO THE QUESTIONS!!!!!

Et

At

bias

MSE

MAD

Percent Error

MAPE

TS

Answer 1

The 4 week Moving Average (MA) forecast

The average of four week are obtained by taking the average of the current year and the previous three year,

Week	Demand	4 week MA
1	108
2	116
3	118
4	124	116.5
5	96	113.5
6	119	114.25
7	96	108.75
8	102	103.25
9	112	107.25
10	102	103
11	92	102
12	91	99.25

The forecast for the next 4 week is the forecast obtained on 12th week. Hence,

Week	4 week MA forecast
13	99.25
14	99.25
15	99.25
16	99.25

Now, the MAD, MAPE, MSE, bias, and TS are estimated using the formula,

Week	At	4 week MA	Ft	Et=Ft-At	|Ft-At|	(Et)^2	Et/At	|Et/At|
1	108
2	116
3	118
4	124	116.5
5	96	113.5	116.5	20.5	20.5	420.25	0.213542	0.213541667
6	119	114.25	113.5	-5.5	5.5	30.25	-0.04622	0.046218487
7	96	108.75	114.25	18.25	18.25	333.0625	0.190104	0.190104167
8	102	103.25	108.75	6.75	6.75	45.5625	0.066176	0.066176471
9	112	107.25	103.25	-8.75	8.75	76.5625	-0.07813	0.078125
10	102	103	107.25	5.25	5.25	27.5625	0.051471	0.051470588
11	92	102	103	11	11	121	0.119565	0.119565217
12	91	99.25	102	11	11	121	0.120879	0.120879121
				BIAS=58.5	MAD=10.875	MSE=146.9062		MAPE=0.11076

The exponential smoothing forecast

For smoothing factor

Forecast for second month is obtained using the formula,,

Similarly the forcast is obtained further till 12th period.

Now, the MAD, MAPE, MSE, bias, and TS are estimated using the formula,

Week	At	Exponential smoothing	Et=Ft-At	|Ft-At|	(Et)^2	Et/At	|Et/At|
1	108	108	0	0	0	0	0
2	116	108	-8	8	64	-0.068965517	0.068965517
3	118	108.8	-9.2	9.2	84.64	-0.077966102	0.077966102
4	124	109.72	-14.28	14.28	203.9184	-0.11516129	0.11516129
5	96	111.148	15.148	15.148	229.461904	0.157791667	0.157791667
6	119	109.6332	-9.3668	9.3668	87.73694224	-0.078712605	0.078712605
7	96	110.56988	14.56988	14.56988	212.2814032	0.151769583	0.151769583
8	102	109.112892	7.112892	7.112892	50.5932326	0.069734235	0.069734235
9	112	108.4016028	-3.5983972	3.5983972	12.94846241	-0.032128546	0.032128546
10	102	108.7614425	6.76144252	6.76144252	45.71710495	0.066288652	0.066288652
11	92	108.0852983	16.08529827	16.08529827	258.7368204	0.174840199	0.174840199
12	91	106.4767684	15.47676844	15.47676844	239.5303614	0.170074378	0.170074378
		104.9290916	BIAS=30.70908	MAD=9.9666	MSE=124.1304		MAPE=0.09695

Week	Forecast
13	104.9290916
14	104.9290916
15	104.9290916
16	104.9290916

The exponential smoothing forecast

For smoothing factor

Now, the MAD, MAPE, MSE, bias, and TS are estimated using the formula,

Week	At	Exponential smoothing	Et=Ft-At	|Ft-At|	(Et)^2	Et/At	|Et/At|
1	108	108	0	0	0	0	0
2	116	108	-8	8	64	-0.068965517	0.068965517
3	118	115.2	-2.8	2.8	7.84	-0.023728814	0.023728814
4	124	117.72	-6.28	6.28	39.4384	-0.050645161	0.050645161
5	96	123.372	27.372	27.372	749.226384	0.285125	0.285125
6	119	98.7372	-20.2628	20.2628	410.5810638	-0.17027563	0.17027563
7	96	116.97372	20.97372	20.97372	439.8969306	0.21847625	0.21847625
8	102	98.097372	-3.902628	3.902628	15.23050531	-0.038261059	0.038261059
9	112	101.6097372	-10.3902628	10.3902628	107.9575611	-0.092770204	0.092770204
10	102	110.9609737	8.96097372	8.96097372	80.29905001	0.087852684	0.087852684
11	92	102.8960974	10.89609737	10.89609737	118.7249379	0.118435841	0.118435841
12	91	93.08960974	2.089609737	2.089609737	4.366468854	0.022962744	0.022962744
		91.20896097	BIAS=18.6567	MAD=10.1606	MSE=169.7967		MAPE=0.098125

Forecast

Week	Forecast
13	91.20896097
14	91.20896097
15	91.20896097
16	91.20896097