Using the data provided: Plot the data. What does the plot tell you about the appropriateness...

Using the data provided:

Plot the data. What does the plot tell you about the appropriateness of using a trend and seasonally adjusted model for your data?
Develop a forecast model that incorporates both a trend and seasonal adjustment (even if its not necessarily there).
Develop a forecast for the four periods beyond your data.
Calculate a MAD and Bias based on the last 12 periods of known data. What do the MAD and bias indicate about your model?
Overall, are you satisfied with your model? If so, why? If not, suggest some things that could be done to improve your model.

data:

*Year*	*Quarter*	*Revenue*
1999	Qtr1	1,939
	Qtr2	2,373
	Qtr3	2,651
	Qtr4	3,111
2000	Qtr1	3,187
	Qtr2	3,634
	Qtr3	3,702
	Qtr4	3,738
2001	Qtr1	3,627
	Qtr2	3,916
	Qtr3	3,588
	Qtr4	2,932
2002	Qtr1	2,931
	Qtr2	3,556
	Qtr3	3,812
	Qtr4	4,085
2003	Qtr1	4,570
	Qtr2	4,189
	Qtr3	4,594
	Qtr4	4,576
2004	Qtr1	5,245
	Qtr2	6,276
	Qtr3	6,558
	Qtr4	7,420

	2004	2003	2002	2001	2000	1999
Qtr1	5,245	4,570	2,931	3,627	3,187	1,933
Qtr2	6,276	4,189	3,556	3,916	3,634	2,373
Qtr3	6,558	4,594	3,812	3,588	3,702	2,651
Qtr4	7,429	4,576	4,085	2,932	3,738	3,111
Year	25,508	17,929	14,384	14,063	14,300	10,068

Expert Solution

Plot of the Raw Data

I don't find any seasonality effect in the data. Definitely, there is a trend. So, my choice is Holt's method. We can implement Holt's method in Minitab (or any other software) or in Excel spreadsheet. I prefer Excel.

				Alpha =	0.99	Beta =	0.1
Period	Revenue (Yt)	At	Tt	Period ahead	Forecast	Absolute Error	Absolute % Error
1	1939	1939.0	0.0
2	2373	2368.7	43.0	1	1939.0	434.0	18.3%
3	2651	2648.6	66.7	1	2411.6	239.4	9.0%
4	3111	3107.0	105.8	1	2715.3	395.7	12.7%
5	3187	3187.3	103.3	1	3212.9	25.9	0.8%
6	3634	3630.6	137.3	1	3290.5	343.5	9.5%
7	3702	3702.7	130.8	1	3767.8	65.8	1.8%
8	3738	3739.0	121.3	1	3833.4	95.4	2.6%
9	3627	3629.3	98.2	1	3860.3	233.3	6.4%
10	3916	3914.1	116.9	1	3727.6	188.4	4.8%
11	3588	3592.4	73.0	1	4031.0	443.0	12.3%
12	2932	2939.3	0.4	1	3665.5	733.5	25.0%
13	2931	2931.1	-0.5	1	2939.7	8.7	0.3%
14	3556	3549.7	61.5	1	2930.6	625.4	17.6%
15	3812	3810.0	81.3	1	3611.2	200.8	5.3%
16	4085	4083.1	100.5	1	3891.3	193.7	4.7%
17	4570	4566.1	138.8	1	4183.6	386.4	8.5%
18	4189	4194.2	87.7	1	4704.9	515.9	12.3%
19	4594	4590.9	118.6	1	4281.8	312.2	6.8%
20	4576	4577.3	105.4	1	4709.5	133.5	2.9%
21	5245	5239.4	161.0	1	4682.7	562.3	10.7%
22	6276	6267.2	247.7	1	5400.4	875.6	14.0%
23	6558	6557.6	252.0	1	6515.0	43.0	0.7%
24	7420	7413.9	312.4	1	6809.6	610.4	8.2%
25				1	7726.3
26				2	8038.7
27				3	8351.2
28				4	8663.6
					MAD =	333.3
					MAPE =		8.5%

Formulation

Determine Bias (With Tracking Signal)

Period	Revenue (Yt)	Forecast	Absolute Error	Error	RSFE	Tracking Signal	Biased?
13	2931	2770.4	160.6	160.6	-443.0	-2.76	Y
14	3556	2813.8	742.2	742.2	299.2	0.40	N
15	3812	3637.0	175.0	175.0	474.2	2.71	Y
16	4085	3938.2	146.8	146.8	621.0	4.23	Y
17	4570	4250.1	319.9	319.9	940.9	2.94	Y
18	4189	4820.3	631.3	-631.3	309.6	0.49	N
19	4594	4269.8	324.2	324.2	633.8	1.95	N
20	4576	4762.9	186.9	-186.9	446.9	2.39	Y
21	5245	4694.2	550.8	550.8	997.8	1.81	N
22	6276	5510.9	765.1	765.1	1762.8	2.30	Y
23	6558	6745.4	187.4	-187.4	1575.4	8.41	Y
24	7420	6975.6	444.4	444.4	2019.8	4.55	Y

Considering an acceptable range of [-2,2] for the tracking signal, we cannot say that the forecast is free from bias.

Overall, the bias is high and the MAPE and MAD are also not very low (e.g. a MAPE below 5% would have been a good estimate). We thus propose a more advanced model such as ARIMA.

orchestra answered 1 year ago

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