Monthly attendance at financial planning seminars for the past 24 months, and forecasts and errors for those months, are shown in the following table. Determine if the forecast is working using these approaches: 1. A tracking signal, beginning with month 10, updating MAD with exponential smoothing

Question

Monthly attendance at financial planning seminars for the past 24 months, and forecasts and errors for those months, are shown in the following table. Determine if the forecast is working using these approaches:

1. A tracking signal, beginning with month 10, updating MAD with exponential smoothing. Use limits of [latex]\pm 4[/latex] and [latex]α = 2[/latex].

2. A control chart with 2s limits. Use data from the first eight months to develop the control chart, and then evaluate the remaining data with the control chart.

Month	A (Attendance)	F (Forecast)	A─ F (Error)	\|e\|	Cumulative \|e\|
1	47	43	4	4	4
2	51	44	7	7	11
3	54	50	4	4	15
4	55	51	4	4	19
5	49	54	-5	5	24
6	46	48	-2	2	26
7	38	46	-8	8	34
8	32	44	-12	12	46
9	25	35	-10	10	56
10	24	26	-2	2	58
11	30	25	5	5
12	35	32	3	3
13	44	34	10	10
14	57	50	7	7
15	60	51	9	9
16	55	54	1	1
17	51	55	-4	4
18	48	51	-3	3
19	42	50	-8	8
20	30	43	-13	13
21	28	38	-10	10
22	25	27	-2	2
23	35	27	8	8
24	38	32	[latex]\frac{6}{-11}[/latex]	6

Accepted Answer

1. The sum of absolute errors through the 10th month is 58. Hence, the initial MAD is 58/10 = 5.8. The subsequent MADs are updated using the formula [latex]MAD_{new}=MAD_{old}+ \alpha (\left|e ight|- MAD_{old} )[/latex]. The results are shown in the following table.

The tracking signal for any month is

[latex]\frac{ ext{Cumulative error at that month}}{ ext{Updated MAD at that month}} [/latex]

Month	A (Attendance)	F (Forecast)	A─ F (Error)	\|e\|	Cumulative \|e\|
1	47	43	4	4	4
2	51	44	7	7	11
3	54	50	4	4	15
4	55	51	4	4	19
5	49	54	-5	5	24
6	46	48	-2	2	26
7	38	46	-8	8	34
8	32	44	-12	12	46
9	25	35	-10	10	56
10	24	26	-2	2	58
11	30	25	5	5
12	35	32	3	3
13	44	34	10	10
14	57	50	7	7
15	60	51	9	9
16	55	54	1	1
17	51	55	-4	4
18	48	51	-3	3
19	42	50	-8	8
20	30	43	-13	13
21	28	38	-10	10
22	25	27	-2	2
23	35	27	8	8
24	38	32	[latex]\frac{6}{-11}[/latex]	6

Because the tracking signal is within [latex]\pm 4[/latex] every month, there is no evidence of a problem.

2. a. Make sure that the average error is approximately zero, because a large average would suggest a biased forecast.

Average error = [latex]\frac{\sum{errors} }{n}= \frac{-11}{24} = -46[/latex]

b. Compute the standard deviation:

[latex]s = \sqrt{MSE}= \sqrt{\frac{\sum{e^2} }{n-1} } [/latex]

= [latex]\sqrt{\frac{4^2+7^2+4^2+4^2+(-5)^2+(-2)^2+(-8)^2+(-12)^2}{8 -1} }=6.91[/latex]

c. Determine 2 s control limits:

[latex]0 \pm 2s = 0 \pm 2(6.91) = -13.82 to + 13.82[/latex]

d. (1) Check that all errors are within the limits. (They are.)

(2) Plot the data (see the following graph), and check for nonrandom patters . Note the strings of positive and negative errors. this suggests nonrandomness (and that an improved forecast is possible). The tracking signal did not reveal this

A plot helps you to visualize the process and enables you to check for possible patterns (i.e, nonrandomness)within the limits that suggest an improved forecast is possible.

Question 3.12: Monthly attendance at financial planning seminars for the pa...

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