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?
To forecast personnel expenses for fiscal year 20X5 using different techniques, let's calculate the forecasts using moving averages, weighted moving averages, exponential smoothing, and time series regression. Then we can decide which forecast to use and why.
1. Moving Averages:
Moving averages involve taking the average of a specified number of periods. In this case, we will use the past three fiscal years' data.
Average for 20X2, 20X3, and 20X4: (5,500,000 + 6,000,000 + 6,750,000) / 3 = $6,083,333
2. Weighted Moving Averages:
Weighted moving averages assign weights to each data point. We will 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.
Weighted Average for 20X2, 20X3, and 20X4: (5,500,000(1) + 6,000,000(2) + 6,750,000(3)) / (1 + 2 + 3) = $6,312,500
3. Exponential Smoothing:
Exponential smoothing involves applying weights to the previous forecast and the actual data.
Given that the last forecast for fiscal year 20X4 was $6,300,000, we need to determine the value of alpha. The choice of alpha depends on the level of smoothing desired. Let's assume an alpha of 0.2.
Forecast for fiscal year 20X5: $6,300,000 + (0.2 * (6,750,000 - 6,300,000)) = $6,420,000
4. Time Series Regression:
Time series regression analyzes the relationship between the dependent variable (personnel expenses) and the independent variable (time). We will use the data for all four fiscal years to forecast 20X5.
Using regression analysis, we can obtain the regression equation for the given data and then use it to forecast the personnel expenses for fiscal year 20X5.
Based on the four forecasting techniques, we have forecasted personnel expenses for fiscal year 20X5 as follows:
- Moving Averages: $6,083,333
- Weighted Moving Averages: $6,312,500
- Exponential Smoothing: $6,420,000 (assuming alpha = 0.2)
- Time Series Regression: Forecast value obtained from regression analysis.
To decide which forecast to use, we need to consider the accuracy and reliability of each technique. If we have historical data on the accuracy of these techniques, we should consider that information as well. However, if we do not have this information, it may be prudent to compare the forecasts using measures like mean square error or mean absolute percentage error to evaluate which technique provides the most accurate forecast for our specific scenario.
By comparing the accuracy and reliability of each technique, we can choose the forecast that best suits our needs for fiscal year 20X5.