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?
What is your college subject?
How would you like us to help you with this assignment?
what is an exponent
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 methods, we will use moving averages, weighted moving averages, exponential smoothing, and time series regression.
1. Moving Averages:
For moving averages, we take the average of the data for the past three fiscal years.
20X2: ($5,250,000 + $5,500,000 + $6,000,000) / 3 = $5,583,333
2. Weighted Moving Averages:
For weighted moving averages, we assign weights to the data for the past three fiscal years and calculate the weighted average.
20X2: ($5,250,000 * 1 + $5,500,000 * 2 + $6,000,000 * 3) / (1 + 2 + 3) = $5,857,143
3. Exponential Smoothing:
To use exponential smoothing, we assume that the last forecast for fiscal year 20X4 was $6,300,000. We also need to choose the value of alpha, which controls the weight given to the most recent data. Let's assume alpha = 0.3.
20X5 Forecast = (1 - alpha) * last forecast + alpha * latest data
20X5 Forecast = (1 - 0.3) * $6,300,000 + 0.3 * $6,750,000 = $6,397,500
4. Time Series Regression:
For time series regression, we will use the data for all four fiscal years to analyze trends and patterns in personnel expenses. We can use regression analysis to create a regression equation that can be used to forecast future values based on past data.
Now, we have four different forecast values for fiscal year 20X5:
- Moving Averages: $5,583,333
- Weighted Moving Averages: $5,857,143
- Exponential Smoothing: $6,397,500
- Time Series Regression: Value depends on the regression analysis.
To decide which forecast to use, we should consider the accuracy and reliability of each method. It is generally recommended to evaluate the performance of different forecasting methods by comparing their accuracy measures, such as mean absolute error (MAE) or mean squared error (MSE). Additionally, it would be beneficial to consider any external factors, such as economic conditions or industry-specific trends, that may impact personnel expenses.
Based on the information provided, it is not stated whether any accuracy measures or external factors are considered. Therefore, it is difficult to conclusively determine which forecast to use. However, it would be a good practice to compare the forecasted values obtained from each method and evaluate their performance and reliability based on known historical data and any other relevant factors.