Question

The past sales history for Store 10 is provided in the table below. Adjust this data using the seasonality index determined using the initial 2 years.  Report the MAPE value for the better of the two forecasts.

That is, if the original trend projection forecast was better according to MAPE, then report that MAPE value.

If however, the Re-Seasonalized forecast is better according to MAPE, then report the MAPE value for that forecast.

Month	Year	Period	Store 10
January	1	1	57823
February	1	2	68337
March	1	3	89769
April	1	4	97923
May	1	5	82921
June	1	6	73146
July	1	7	60618
August	1	8	52359
September	1	9	34206
October	1	10	37112
November	1	11	42595
December	1	12	58671
January	2	13	61051
February	2	14	76957
March	2	15	96179
April	2	16	108121
May	2	17	92022
June	2	18	85578
July	2	19	74656
August	2	20	62017
September	2	21	49195
October	2	22	48937
November	2	23	57760
December	2	24	67649

You have now moved through the next year and have the sales data available for this year:

Month	Year	Period	Store 10
January	3	25	78129
February	3	26	88549
March	3	27	96211
April	3	28	111863
May	3	29	98494
June	3	30	88820
July	3	31	78414
August	3	32	61967
September	3	33	40984
October	3	34	52707
November	3	35	58102
December	3	36	68250

Use only Year 1 and Year 2 to create the forecast, then compare that forecast to the sales for Year 3.

Answer 1

Trend projection without seasonal adjustment and re-adjustment

Month	Year	Period	Actual	Trend	|Error| / Actual
Jan	1	1	57823	69873	20.84%
Feb	1	2	68337	69723	2.03%
Mar	1	3	89769	69573	22.50%
Apr	1	4	97923	69423	29.10%
May	1	5	82921	69273	16.46%
Jun	1	6	73146	69124	5.50%
Jul	1	7	60618	68974	13.78%
Aug	1	8	52359	68824	31.45%
Sep	1	9	34206	68674	100.77%
Oct	1	10	37112	68525	84.64%
Nov	1	11	42595	68375	60.52%
Dec	1	12	58671	68225	16.28%
Jan	2	13	61051	68075	11.51%
Feb	2	14	76957	67925	11.74%
Mar	2	15	96179	67776	29.53%
Apr	2	16	108121	67626	37.45%
May	2	17	92022	67476	26.67%
Jun	2	18	85578	67326	21.33%
Jul	2	19	74656	67176	10.02%
Aug	2	20	62017	67027	8.08%
Sep	2	21	49195	66877	35.94%
Oct	2	22	48937	66727	36.35%
Nov	2	23	57760	66577	15.27%
Dec	2	24	67649	66428	1.81%
				MAPE	27.07%

Seasonal adjustment --> Trend projection --> Re-seasonalize

Month	Year	Period	Actual	Seasonal averages	Seasonal indices	Deseasonalized data	Trend	Re-seasonalized forecast	|Error| / Actual
Jan	1	1	57823	59437.0	0.872	66299.5	59740	52102	9.89%
Feb	1	2	68337	72647.0	1.066	64106.9	60472	64462	5.67%
Mar	1	3	89769	92974.0	1.364	65800.8	61203	83496	6.99%
Apr	1	4	97923	103022.0	1.512	64777.0	61934	93625	4.39%
May	1	5	82921	87471.5	1.284	64604.7	62665	80432	3.00%
Jun	1	6	73146	79362.0	1.165	62812.3	63397	73827	0.93%
Jul	1	7	60618	67637.0	0.992	61077.8	64128	63645	4.99%
Aug	1	8	52359	57188.0	0.839	62395.4	64859	54427	3.95%
Sep	1	9	34206	41700.5	0.612	55902.0	65591	40134	17.33%
Oct	1	10	37112	43024.5	0.631	58784.8	66322	41870	12.82%
Nov	1	11	42595	50177.5	0.736	57851.7	67053	49370	15.91%
Dec	1	12	58671	63160.0	0.927	63306.4	67784	62821	7.07%
Jan	2	13	61051		0.872	70000.7	68516	59756	2.12%
Feb	2	14	76957	68150.1	1.066	72193.3	69247	73816	4.08%
Mar	2	15	96179		1.364	70499.4	69978	95468	0.74%
Apr	2	16	108121		1.512	71523.1	70710	106891	1.14%
May	2	17	92022		1.284	71695.4	71441	91695	0.36%
Jun	2	18	85578		1.165	73487.9	72172	84046	1.79%
Jul	2	19	74656		0.992	75222.3	72903	72355	3.08%
Aug	2	20	62017		0.839	73904.7	73635	61790	0.37%
Sep	2	21	49195		0.612	80398.2	74366	45504	7.50%
Oct	2	22	48937		0.631	77515.4	75097	47410	3.12%
Nov	2	23	57760		0.736	78448.5	75829	55831	3.34%
Dec	2	24	67649		0.927	72993.7	76560	70954	4.89%
								MAPE	5.23%

Calculations

It is noted that the MAPE for the seasonality adjusted forecast is much smaller.

Comparison with actual data for the next year and the forecasted data

Month	Year	Period	Actual	Seasonal averages	Seasonal indices	Deseasonalized data	Trend	Re-seasonalized forecast
Jan	3	25	78129		0.872		77291	67409
Feb	3	26	88549		1.066		78022	83171
Mar	3	27	96211		1.364		78754	107440
Apr	3	28	111863		1.512		79485	120157
May	3	29	98494		1.284		80216	102959
Jun	3	30	88820		1.165		80948	94265
Jul	3	31	78414		0.992		81679	81064
Aug	3	32	61967		0.839		82410	69154
Sep	3	33	40984		0.612		83141	50874
Oct	3	34	52707		0.631		83873	52951
Nov	3	35	58102		0.736		84604	62292
Dec	3	36	68250		0.927		85335	79087