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 280 312 348 380 416 452 460 469 472 456 a) Prepare a forecast for admissions for years 4 through 11 by using a three-year moving average method. b) Calculate the mean squared error (MSE) for the three-year moving average method, with error measurement beginning in year 4. c) Assume that the initial forecast for year 1 is 270 admissions. Prepare a forecast for admissions for years 2 through 11 by using an exponential smoothing method with  = 0.60. d) Calculate the mean squared error (MSE) for the exponential smoothing method with  = 0.60, with error measurement beginning in year 4. e) 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

(a) Let the actual admissions for period t be At and the forecast be Ft

For 3 period moving average, Ft = (A_t-1 + A_t-2 + A_t-3)/3

Calculating using the above -

Year	Admissions	Forecast
1	280
2	312
3	348
4	380	313.33
5	416	346.67
6	452	381.33
7	460	416.00
8	469	442.67
9	472	460.33
10	456	467.00
11		465.67

(b) Squared error = (A_t - F_t)²

Mean squared error = Σ (A_t - F_t)² /n

Year	Admissions	Forecast	Squared Error
1	280
2	312
3	348
4	380	313.33	4444.44
5	416	346.67	4807.11
6	452	381.33	4993.78
7	460	416.00	1936.00
8	469	442.67	693.44
9	472	460.33	136.11
10	456	467.00	121.00
11		465.67
		MSE	2447.41

Hence, MSE = 2447.41

(c) For exponential forecasting, F_t = F_t-1 + ? (A_t-1 - F_t-1)

where, ? = 0.60

Given F₁ = 270

Year	Admissions	Forecast
1	280	270
2	312	276
3	348	297.6
4	380	327.84
5	416	359.14
6	452	393.25
7	460	428.50
8	469	447.40
9	472	460.36
10	456	467.34
11		460.54

(d)  

Squared error = (A_t - F_t)²

Mean squared error = Σ (A_t - F_t)² /n

Year	Admissions	Forecast	Squared Error
1	280	270
2	312	276
3	348	297.6
4	380	327.84	2720.67
5	416	359.14	3233.51
6	452	393.25	3451.05
7	460	428.50	992.14
8	469	447.40	466.53
9	472	460.36	135.48
10	456	467.34	128.69
11		460.54
		MSE	1589.72

MSE = 1589.72

(e) Exponential forecasting method would be preferred, since the MSE is lower for exponential forecasting as compared to moving average