Question

CoastCo Insurance, Inc., is interested in developing a forecast of larceny thefts in the United States. It has found the following data:

(c1p11)	Year	Larceny Thefts*	Year	Larceny Thefts*
	1	4,151	10	7,194
	2	4,348	11	7,143
	3	5,263	12	6,713
	4	5,978	13	6,592
	5	6,271	14	6,926
	6	5,906	15	7,257
	7	5,983	16	7,500
	8	6,578	17	7,706
	9	7,137	18	7,872

Plot this series in a time-series plot and make a naive forecast for years 2 through 19. Calculate the MAPE for years 2 through 18. On the basis of these measures and what you see in the plot, what do you think of your forecast? Explain. (Please show work)

Answer 1

The time series plot is:

The MAPE calculation is as below:

The formulas are:

The output is:

Year	Larceny Thefts*	Forecast	Error	Absolute Error	% Error
1	4,151
2	4,348	4,151	197	197	4.53
3	5,263	4,348	915	915	17.39
4	5,978	5,263	715	715	11.96
5	6,271	5,978	293	293	4.67
6	5,906	6,271	-365	365	6.18
7	5,983	5,906	77	77	1.29
8	6,578	5,983	595	595	9.05
9	7,137	6,578	559	559	7.83
10	7,194	7,137	57	57	0.79
11	7,143	7,194	-51	51	0.71
12	6,713	7,143	-430	430	6.41
13	6,592	6,713	-121	121	1.84
14	6,926	6,592	334	334	4.82
15	7,257	6,926	331	331	4.56
16	7,500	7,257	243	243	3.24
17	7,706	7,500	206	206	2.67
18	7,872	7,706	166	166	2.11
19		7,872		MAPE	5.30

The time series plot is:

From the above plot and also from the calculations, it is clear that the forecast figures are most of the times less than the actual figure. Therefore, the method has a considerable amount of bias associated with it. The value of MAPE is low and hence the accuracy is good.