Exponential Smothing Techniques for Forecasting

Exponential Smothing Techniques
Ft=αD(t-1) + (1-α)Ft-1
		α=0.1
Time Period	Sales(Di)	Fi	(Fi-Di)	Σ(Fi-Di)	Σ│Fi-Di│	Average Di
1	1084	1084	0
2	1056	1084	28
3	1090	1081.2	-8.8
4	953	1082.08	129.08
5	858	1069.172	211.172
6	868	1048.055	180.0548
7	1034	1030.049	-3.95068
8	1088	1030.444	-57.555612
9	1069	1036.2	-32.800051
10	856	1039.48	183.479954
11	876	1021.132	145.131959
12	796	1006.619	210.618763	1704.671	2395.544	937.041
13	1023	985.5569	-37.443113
14	1003	989.3012	-13.698802
15	1036	990.6711	-45.328922
16	835	995.204	160.20397
17	747	979.1836	232.183573
18	856	955.9652	99.965216
19	1008	945.9687	-62.031306
20	1036	952.1718	-83.828175
21	920	960.5546	40.5546425
22	805	956.4992	151.499178
23	816	941.3493	125.34926
24	776	928.8143	152.814334
25	X	913.5329	X
MAD					99.8143333
CV					12.8626718
BIAS				71.02796
Exponential Smothing Techniques
Ft=αD(t-1) + (1-α)Ft-1
		α=0.2
Time Period	Sales(Di)	Fi	(Fi-Di)	Σ(Fi-Di)	Σ│Fi-Di│	Di
1	1084	1084	0
2	1056	1084	28
3	1090	1078.4	-11.6
4	953	1080.72	127.72
5	858	1055.176	197.176
6	868	1015.741	147.7408
7	1034	986.1926	-47.80736
8	1088	995.7541	-92.245888
9	1069	1014.203	-54.79671
10	856	1025.163	169.162632
11	876	991.3301	115.330105
12	796	968.2641	172.264084	1073.695	2368.9569	937.041
13	1023	933.8113	-89.188733
14	1003	951.649	-51.350986
15	1036	961.9192	-74.080789
16	835	976.7354	141.735369
17	747	948.3883	201.388295
18	856	908.1106	52.1106361
19	1008	897.6885	-110.31149
20	1036	919.7508	-116.24919
21	920	943.0006	23.0006457
22	805	938.4005	133.400517
23	816	911.7204	95.7204132
24	776	892.5763	116.576331
25	X	869.2611	X
MAD					98.7065375
CV					10.5338547
BIAS				44.73728
Exponential Smothing Techniques
Ft=αD(t-1) + (1-α)Ft-1
		α=0.3
Time Period	Sales(Di)	Fi	(Fi-Di)	Σ(Fi-Di)	Σ│Fi-Di│	Di
1	1084	1084	0
2	1056	1084	28
3	1090	1075.6	-14.4
4	953	1079.92	126.92
5	858	1041.844	183.844
6	868	986.6908	118.6908
7	1034	951.0836	-82.91644
8	1088	975.9585	-112.04151
9	1069	1009.571	-59.429056
10	856	1027.4	171.399661
11	876	975.9798	99.9797628
12	796	945.9858	149.985834	795.6667	2381.1651	937.041
13	1023	900.9901	-122.00992
14	1003	937.5931	-65.406941
15	1036	957.2151	-78.784859
16	835	980.8506	145.850599
17	747	937.0954	190.095419
18	856	880.0668	24.0667934
19	1008	872.8468	-135.15324
20	1036	913.3927	-122.60727
21	920	950.1749	30.1749101
22	805	941.1224	136.122437
23	816	900.2857	84.285706
24	776	875	98.9999942
25	X	845.3	X
MAD					99.2152125
CV					10.58814
BIAS				33.15278
Exponential Smothing Techniques
Ft=αD(t-1) + (1-α)Ft-1
		α=0.4
Time Period	Sales(Di)	Fi	(Fi-Di)	Σ(Fi-Di)	Σ│Fi-Di│	Di
1	1084	1084	0
2	1056	1084	28
3	1090	1072.8	-17.2
4	953	1079.68	126.68
5	858	1029.008	171.008
6	868	960.6048	92.6048
7	1034	923.5629	-110.43712
8	1088	967.7377	-120.26227
9	1069	1015.843	-53.157363
10	856	1037.106	181.105582
11	876	964.6633	88.6633492
12	796	929.198	133.19801
13	1023	875.9188	-147.08119	643.3754	2366.088	937.041
14	1003	934.7513	-68.248717
15	1036	962.0508	-73.94923
16	835	991.6305	156.630462
17	747	928.9783	181.978277
18	856	856.187	0.18696633
19	1008	856.1122	-151.88782
20	1036	916.8673	-119.13269
21	920	964.5204	44.5203847
22	805	946.7122	141.712231
23	816	890.0273	74.0273385
24	776	860.4164	84.4164031
25	X	826.6498	X
MAD					98.587
CV					10.5210978
BIAS				26.80731
Exponential Smothing Techniques
Ft=αD(t-1) + (1-α)Ft-1
		α=0.5
Time Period	Sales(Di)	Fi	(Fi-Di)	Σ(Fi-Di)	Σ│Fi-Di│	Di
1	1084	1084	0
2	1056	1084	28
3	1090	1070	-20
4	953	1080	127
5	858	1016.5	158.5
6	868	937.25	69.25
7	1034	902.625	-131.375
8	1088	968.3125	-119.6875
9	1069	1028.156	-40.84375
10	856	1048.578	192.578125
11	876	952.2891	76.2890625
12	796	914.1445	118.144531	545.1074	2354.721	937.041
13	1023	855.0723	-167.92773
14	1003	939.0361	-63.963867
15	1036	971.0181	-64.981934
16	835	1003.509	168.509033
17	747	919.2545	172.254517
18	856	833.1273	-22.872742
19	1008	844.5636	-163.43637
20	1036	926.2818	-109.71819
21	920	981.1409	61.1409073
22	805	950.5705	145.570454
23	816	877.7852	61.7852268
24	776	846.8926	70.8926134
25	X	811.4463	X
MAD					98.113375
CV					10.470553
BIAS				22.71281
Exponential Smothing Techniques
Ft=αD(t-1) + (1-α)Ft-1
		α=0.6
Time Period	Sales(Di)	Fi	(Fi-Di)	Σ(Fi-Di)	Σ│Fi-Di│	Di
1	1084	1084	0
2	1056	1084	28
3	1090	1067.2	-22.8
4	953	1080.88	127.88
5	858	1004.152	146.152
6	868	916.4608	48.4608
7	1034	887.3843	-146.61568
8	1088	975.3537	-112.64627
9	1069	1042.941	-26.058509
10	856	1058.577	202.576596
11	876	937.0306	61.0306386
12	796	900.4123	104.412255
13	1023	837.7649	-185.2351	474.0228	2300.624	937.041
14	1003	948.906	-54.094039
15	1036	981.3624	-54.637616
16	835	1014.145	179.144954
17	747	906.658	159.657981
18	856	810.8632	-45.136807
19	1008	837.9453	-170.05472
20	1036	939.9781	-96.021889
21	920	997.5912	77.5912443
22	805	951.0365	146.036498
23	816	863.4146	47.4145991
24	776	834.9658	58.9658396
25	X	799.5863	X
MAD					95.8593333
CV					10.2300042
BIAS				19.75095
Exponential Smothing Techniques
Ft=αD(t-1) + (1-α)Ft-1
		α=0.7
Time Period	Sales(Di)	Fi	(Fi-Di)	Σ(Fi-Di)	Σ│Fi-Di│	Di
1	1084	1084	0
2	1056	1084	28
3	1090	1064.4	-25.6
4	953	1082.32	129.32
5	858	991.796	133.796
6	868	898.1388	30.1388
7	1034	877.0416	-156.95836
8	1088	986.9125	-101.08751
9	1069	1057.674	-11.326252
10	856	1065.602	209.602124
11	876	918.8806	42.8806373
12	796	888.8642	92.8641912
13	1023	823.8593	-199.14074	418.7695	2210.2346	937.041
14	1003	963.2578	-39.742223
15	1036	991.0773	-44.922667
16	835	1022.523	187.5232
17	747	891.257	144.25696
18	856	790.2771	-65.722912
19	1008	836.2831	-171.71687
20	1036	956.4849	-79.515062
21	920	1012.145	92.1454814
22	805	947.6436	142.643644
23	816	847.7931	31.7930933
24	776	825.5379	49.537928
25	X	790.8614	X
MAD					92.0931083
CV					9.82807672
BIAS				17.44873
Exponential Smothing Techniques
Ft=αD(t-1) + (1-α)Ft-1
		α=0.8
Time Period	Sales(Di)	Fi	(Fi-Di)	Σ(Fi-Di)	Σ│Fi-Di│	Di
1	1084	1084	0
2	1056	1084	-28
3	1090	1061.6	28.4
4	953	1084.32	-131.32
5	858	979.264	-121.264
6	868	882.2528	-14.2528
7	1034	870.8506	163.14944
8	1088	1001.37	86.629888
9	1069	1070.674	-1.6740224
10	856	1069.335	-213.3348
11	876	898.667	-22.666961
12	796	880.5334	-84.533392	-374.2	2097.857	937.041
13	1023	812.9067	210.093322
14	1003	980.9813	22.0186643
15	1036	998.5963	37.4037329
16	835	1028.519	-193.51925
17	747	873.7039	-126.70385
18	856	772.3408	83.6592299
19	1008	839.2682	168.731846
20	1036	974.2536	61.7463692
21	920	1023.651	-103.65073
22	805	940.7301	-135.73015
23	816	832.146	-16.146029
24	776	819.2292	-43.229206
25	X	784.6458	X
MAD					87.4107083
CV					9.32837606
BIAS				-15.5914
Exponential Smothing Techniques
Ft=αD(t-1) + (1-α)Ft-1
		α=0.9
Time Period	Sales(Di)	Fi	(Fi-Di)	Σ(Fi-Di)	Σ│Fi-Di│	Di
1	1084	1084	0
2	1056	1084	28
3	1090	1058.8	-31.2
4	953	1086.88	133.88
5	858	966.388	108.388
6	868	868.8388	0.8388
7	1034	868.0839	-165.91612
8	1088	1017.408	-70.591612
9	1069	1080.941	11.9408388
10	856	1070.194	214.194084
11	876	877.4194	1.41940839
12	796	876.1419	80.1419408
13	1023	804.0142	-218.98581	337.7598	1989.779	937.041
14	1003	1001.101	-1.8985806
15	1036	1002.81	-33.189858
16	835	1032.681	197.681014
17	747	854.7681	107.768101
18	856	757.7768	-98.22319
19	1008	846.1777	-161.82232
20	1036	991.8178	-44.182232
21	920	1031.582	111.581777
22	805	931.1582	126.158178
23	816	817.6158	1.61581777
24	776	816.1616	40.1615818
25	X	780.0162	X
MAD					82.9074583
CV					8.8477941
BIAS				14.07333