To calculate the Mean Absolute Deviation (MAD), we first need to compute the absolute deviations between the actual values and the forecasted values, and then take the average of those absolute deviations.
Here’s the input data you provided:
| Week | Time Series Value (Actual) | Forecast | |------|----------------------------|----------| | 1 | 4 | | | 2 | 6 | 7.00 | | 3 | 5 | 8.00 | | 4 | 4 | 5.00 | | 5 | 7 | 5.00 |
Step 1: Calculate the Absolute Deviations
- Week 2: |6 - 7.00| = 1.00
- Week 3: |5 - 8.00| = 3.00
- Week 4: |4 - 5.00| = 1.00
- Week 5: |7 - 5.00| = 2.00
Step 2: Sum the Absolute Deviations
Sum = 1.00 + 3.00 + 1.00 + 2.00 = 7.00
Step 3: Calculate the Mean Absolute Deviation (MAD)
The formula for MAD is:
\[ \text{MAD} = \frac{\text{Sum of Absolute Deviations}}{\text{Number of Forecasts}} \]
Since we have forecasts for Weeks 2, 3, 4, and 5, we have 4 forecasts.
\[ \text{MAD} = \frac{7.00}{4} = 1.75 \]
Thus, the value of MAD is 1.75.