(a) To calculate the 3-week moving average, we first need to find the average of the first three values, then shift the window by one and find the average again, and so on.
Week 1-3 average = (8+13+15)/3 = 12
Week 2-4 average = (13+15+17)/3 = 15
Week 3-5 average = (15+17+16)/3 = 16
Week 4-6 average = (17+16+9)/3 = 14
Therefore, forecast for week 7 using the 3-week moving average is 14.
(b) To compute the Mean Squared Error (MSE) for the 3-week moving average, we need to calculate the squared difference between the actual value and the forecast, then find the average of those squared differences.
MSE = ((8-14)^2 + (13-14)^2 + (15-14)^2 + (17-14)^2 + (16-14)^2 + (9-14)^2) / 6
MSE = (36 + 1 + 1 + 9 + 4 + 25) / 6
MSE = 76 / 6
MSE = 12.67
(c) To compute the exponential smoothing values using Alpha = 0.2, we first assign the first observation as the initial forecast. Then, we use the formula: Forecast = Alpha * Actual + (1 - Alpha) * Previous Forecast.
For week 1, Forecast = 0.2 * 8 + (1 - 0.2) * 8 = 1.6 + 6.4 = 8
For week 2, Forecast = 0.2 * 13 + (1 - 0.2) * 8 = 2.6 + 6.4 = 9
For week 3, Forecast = 0.2 * 15 + (1 - 0.2) * 9 = 3 + 7.2 = 10.2
For week 4, Forecast = 0.2 * 17 + (1 - 0.2) * 10.2 = 3.4 + 8.16 = 11.56
For week 5, Forecast = 0.2 * 16 + (1 - 0.2) * 11.56 = 3.2 + 9.248 = 12.448
For week 6, Forecast = 0.2 * 9 + (1 - 0.2) * 12.448 = 1.8 + 9.9584 = 11.7584
Therefore, the forecast for week 7 using exponential smoothing with Alpha = 0.2 is 11.76.
(d) Comparing the 3-week moving average forecast (14) with the exponential smoothing forecast with Alpha = 0.2 (11.76), it appears that the exponential smoothing forecast provides a better forecast as it has a lower error value.
(e) Now, let's compute the exponential smoothing values using Alpha = 0.4.
For week 1, Forecast = 0.4 * 8 + (1 - 0.4) * 8 = 3.2 + 4.8 = 8
For week 2, Forecast = 0.4 * 13 + (1 - 0.4) * 8 = 5.2 + 4.8 = 10
For week 3, Forecast = 0.4 * 15 + (1 - 0.4) * 10 = 6 + 6 = 12
For week 4, Forecast = 0.4 * 17 + (1 - 0.4) * 12 = 6.8 + 7.2 = 14
For week 5, Forecast = 0.4 * 16 + (1 - 0.4) * 14 = 6.4 + 8.4 = 14.8
For week 6, Forecast = 0.4 * 9 + (1 - 0.4) * 14.8 = 3.6 + 8.88 = 12.48
For week 7, Forecast = 0.4 * Forecast(week 6) + (1 - 0.4) * Actual(week 7) = 0.4 * 12.48 + 0.6 * 9 = 4.992 + 5.4 = 10.392
Therefore, the forecast for week 7 using exponential smoothing with Alpha = 0.4 is 10.392.
Comparing the forecasts from Alpha = 0.2 (11.76) and Alpha = 0.4 (10.392), it appears that Alpha = 0.4 provides a better forecast as it has a lower error value. A higher value of Alpha gives more weight to recent observations and reacts more quickly to changes, which in this case results in a better forecast compared to Alpha = 0.2.
Activity
Step by step and by showing your work answer the questions below.
1. Consider the following time series data.
Week 1 2 3 4 5 6
Value 8 13 15 17 16 9
(a) Develop a 3- week moving average for this time series. What is the forecast for
week 7?
(b) Compute the MSE for the 3-week moving average.
(c) Use
Alpha = .2
to compute the exponential smoothing values for the time series.
What is the forecast for week 7?
(d) Compare the 3-week moving average forecast with the exponential smoothing
forecast using
Alpha = .2
. Which appears to provide the better forecast?
(e) Use a smoothing constant of .4 to compute the exponential smoothing values.
Does a smoothing constant of .2 or .4 appear to provide the better forecast?
Explain
1 answer
1 answer