Week 5 – Forecasting
Exercise 9.1
The following data represent total personnel expenses for the Palmdale Human
Service Agency for past four fiscal years:
20X1 $5,250,000
20X2 $5,500,000
20X3 $6,000,000
20X4 $6,750,000
Forecast personnel expenses for fiscal year 20X5 using moving averages, weighted moving averages, exponential smoothing, and time series regression. For moving averages and weighted moving averages, use only the data for the past three fiscal years. For weighted moving averages, assign a value of 1 to the data for 20X2, a value of 2 to the data for 20X3, and a value of 3 to the data for 20X4. For exponential smoothing, assume that the last forecast for fiscal year 20X4 was $6,300,000.
You decide on the alpha to be used for exponential smoothing. For time series regression, use the data for all four fiscal years. Which forecast will you use? Why?
Moving Average for fiscal year 20X5 = $6,083,333
20X2 + 20X3 + 20X4 / 3 = 20X5 moving average forecast
5,500,000+6,000,000+6,750,000=18,250,000
18,250,000/3=6,083,333
Weighted moving averages for fiscal year 20X5 = $6,291,667
20X2(1) + 20X3(2) + 20X4(3) / 6 = 20X5 weighted moving average forecast
5,500,000(1) = 5,500,000 +
6,000,000(2) = 12,000,000 +
6,750,000(3) = 20,250,000 = 37,750,000 / 6 = 6,291,667
Exponential smoothing for fiscal year 20X5 = $6,210,000
Use formula NF = LF + a (LD - LF)
NF = New forecast; LF = Last forecast; α = 0 to 1; LD = Last data
NF = 6,300,000 + .3(6,000,000 – 6,300,000)
NF = 6,210,000
Time Series Regression for fiscal year 20X5 = $7,125,000
Computer output: Constant = 4625000, Variable = 500000, R-Square = 0.95
Use formula Y = A + BX
Y = 462,500 + 500,000X
Y = 462,500 + 500,000 (5)
Y = 462,500 + 2,500,000
Y = 7,125,000
I choose to use the time series regression because it reveals that the expenses will continue to grow on 20X5 and the years after 20X5.
Exercise 9.3
The following data represent total revenues (from all sources)...