Question

use below data:

Year	Month	Demand (u)
2017	May	147
2017	June	181
2017	July	154
2017	August	215
2017	September	179
2017	October	166
2017	November	227
2017	December	245
2018	January	223
2018	February	271
2018	March	260
2018	April	248
2018	May	316
2018	June	272
2018	July	378
2018	August	355
2018	September	371
2018	October	366
2018	November	426
2018	December	418

You plan to use an exponential smoothing method to forecast demand.

Find the MSE if you the exponential smoothing with alpha of 0.15

and the MSE if you use the exponential smoothing with alpha of 0.47.

Which of the above models is relatively more accurate according to

the value of MSE? Give a brief explanation.

Answer 1

The formula for exponential smoothing is,
Forecast = Previous forecast + alpha*(previous actual demand- Previous forecast)

Year	Month	Demand (u)	Forecast at Alpha =0.15	Error	SSE	Forecast at Alpha =0.47	Error	SSE
2017	May	147	147.00	0.00	0.00	147	0	0.00
2017	June	181	147.00	34.00	1156.00	147	34	1156.00
2017	July	154	152.10	1.90	3.61	163	-8.98	80.64
2017	August	215	152.39	62.62	3920.64	159	56.24	3162.94
2017	September	179	161.78	17.22	296.62	185	-6.19	38.32
2017	October	166	164.36	1.64	2.69	182	-16.28	265.04
2017	November	227	164.61	62.39	3892.94	175	52.37	2742.62
2017	December	245	173.97	71.03	5045.89	199	45.76	2093.98
2018	January	223	184.62	38.38	1472.97	221	2.25	5.06
2018	February	271	190.38	80.62	6499.97	222	49.19	2419.66
2018	March	260	202.47	57.53	3309.59	245	15.07	227.10
2018	April	248	211.10	36.90	1361.59	252	-4.01	16.08
2018	May	316	216.64	99.36	9873.35	250	65.87	4338.86
2018	June	272	231.54	40.46	1637.01	281	-9.09	82.63
2018	July	378	237.61	140.39	19709.63	277	101.2	10237.39
2018	August	355	258.67	96.33	9279.92	324	30.63	938.20
2018	September	371	273.12	97.88	9580.98	339	32.23	1038.77
2018	October	366	287.80	78.20	6115.26	354	12.08	145.93
2018	November	426	299.53	126.47	15994.69	360	66.4	4408.96
2018	December	418	318.50	99.50	9900.17	391	27.19	739.30
				MSE	5452.68		MSE	1706.87

Error = Demand-Forecast

SSE = Error^2

MSE = SSE/20

By looking at the MSE, the error is low at alpha = 0.47 as it gives more weight to the difference to previous actual demand and previous forecast