Question

An intensive care unit manager would like to forecast the number of inpatient admissions for the next year. Inpatient admissions for the unit over the past 10 years are shown in the following table.

Year	1	2	3	4	5	6	7	8	9	10
Admissions	321	345	330	368	405	395	456	469	474	465

1. Prepare a forecast for admissions for years 4 through 11 by using a three-year moving average method.
2. Calculate the mean squared error (MSE) for the three-year moving average method, with error measurement beginning in year 4.
3. Assume that the initial forecast for year 1 is 340 admissions. Prepare a forecast for admissions for years 2 through 11 by using an exponential smoothing method with         a = 0.30.
4. Calculate the mean squared error (MSE) for the exponential smoothing method with
   a = 0.30, with error measurement beginning in year 4.
5. Compare the performance of the two forecasting methods by using MSE as the performance criterion. Which method would you recommend based on MSE? Why?

Answer 1

Prepare a forecast for admissions for years 4 through 11 by using a three-year moving average method.

We prepare this by first taking total of preceding 3 years of the forecast year(since 3-yer moving average). Then we divide it by 3.

Year	Admissions	3 moving total	Average
1	321
2	345
3	330
4	368	321+345+330 = 996	996/3 = 332.000
5	405	1043	347.667
6	395	1103	367.667
7	456	1168	389.333
8	469	1256	418.667
9	474	1320	440.000
10	465	1399	466.333
11		1408	469.333

Calculate the mean squared error (MSE) for the three-year moving average method, with error measurement beginning in year 4.

We calculate the error (Actual (A)- forecast (F)) and then square it. We divide this by 7 (Since we we have forecast for 7 years).

Year	Admissions	3 moving total	Average (F)	Error	Error^2
1	321
2	345
3	330
4	368	996	332.000	36.000	1296.000
5	405	1043	347.667	57.333	3287.111
6	395	1103	367.667	27.333	747.111
7	456	1168	389.333	66.667	4444.444
8	469	1256	418.667	50.333	2533.444
9	474	1320	440.000	34.000	1156.000
10	465	1399	466.333	-1.333	1.778
Total					13465.889

.Mean squared error = = 13465.889 / 7

Assume that the initial forecast for year 1 is 340 admissions. Prepare a forecast for admissions for years 2 through 11 by using an exponential smoothing method with          = 0.30.

We have the following formula for forecasting

Year	Admissions (A)	Forecast (F)
1	321	340.000
2	345	334.300
3	330	337.510
4	368	335.257
5	405	345.080
6	395	363.056
7	456	372.639
8	469	397.647
9	474	419.053
10	465	435.537
11		444.376

Calculate the mean squared error (MSE) for the exponential smoothing method with
a = 0.30, with error measurement beginning in year 4.

It is calculated the same way as moving average.

Year	Admissions (A)	Forecast (F)	Error	Error^2
1	321	340.000
2	345	334.300
3	330	337.510
4	368	335.257	32.743	1072.104
5	405	345.080	59.920	3590.418
6	395	363.056	31.944	1020.424
7	456	372.639	83.361	6949.031
8	469	397.647	71.353	5091.193
9	474	419.053	54.947	3019.153
10	465	435.537	29.463	868.055
Total				21610.377

MSE = 21610.377 / 7

Compare the performance of the two forecasting methods by using MSE as the performance criterion. Which method would you recommend based on MSE? Why?

MSE of 3 year moving avg (1923.698) > MSE of exponential smoothing (3087.197)

We can conclude that the 3 -year moving average method is better for forecasting since it produces less error. (The is less variation between the actual and the forecast values)