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, we can use four different methods: moving averages, weighted moving averages, exponential smoothing, and time series regression. Let's go through each method and see which forecast will be the most appropriate.
1. Moving Averages:
For moving averages, we need to use only the data for the past three fiscal years. So, using the total personnel expenses for 20X2, 20X3, and 20X4, we can calculate the average and use it as the forecast for fiscal year 20X5.
Average = (Total expenses for 20X2 + Total expenses for 20X3 + Total expenses for 20X4) / 3
2. Weighted Moving Averages:
Similar to moving averages, weighted moving averages also use the data for the past three fiscal years. Additionally, we assign weights to the data based on their relative importance or significance. In this case, we assign a value of 1 to 20X2, 2 to 20X3, and 3 to 20X4. Then, we calculate the weighted average, which will be our forecast for fiscal year 20X5.
Weighted Average = (Total expenses for 20X2 * 1 + Total expenses for 20X3 * 2 + Total expenses for 20X4 * 3) / (1+2+3)
3. Exponential Smoothing:
For exponential smoothing, we need to consider the previous forecast as well. In this case, the last forecast for 20X4 was $6,300,000. We also need to choose a value for alpha, which represents the smoothing factor. A higher alpha will give more weight to recent data. Given that we don't have any specific information or guidelines for alpha, we'll make an assumption.
4. Time Series Regression:
Time series regression uses the data for all four fiscal years to forecast. It considers the relationship between the independent variable (fiscal year) and the dependent variable (personnel expenses) to develop a regression equation. Then, we can use this equation to predict the personnel expenses for fiscal year 20X5.
Which forecast to use:
The forecast method to use depends on several factors such as the stability of the data, the significance of recent data, and the available historical pattern. Each method has its own pros and cons, and it's important to consider these factors before making a decision.
Without additional information, it is challenging to determine which forecast will be the most appropriate. However, if the data is stable and the historical pattern indicates a consistent increase, time series regression might be a suitable method. On the other hand, if recent data is considered more significant, exponential smoothing could provide a good forecast. Ultimately, the choice of forecast method should be based on a thorough analysis of the data and consideration of other contextual factors.