To calculate the bias using the naïve forecast method, we first need to understand what the naïve forecast is. The naïve forecast for a given period is simply the value of the previous period.
For the data provided:
- Week 1: 5 (no previous value, so no forecast needed)
- Week 2: 17 (naïve forecast = Week 1 value = 5)
- Week 3: 24 (naïve forecast = Week 2 value = 17)
- Week 4: 18 (naïve forecast = Week 3 value = 24)
Step 1: Calculate the Forecasts
- Week 2 Forecast = Week 1 Value = 5
- Week 3 Forecast = Week 2 Value = 17
- Week 4 Forecast = Week 3 Value = 24
Step 2: Calculate the Forecast Errors
The forecast error for each week is calculated by subtracting the forecast value from the actual value:
- Week 2 Error: Actual (17) - Forecast (5) = 12
- Week 3 Error: Actual (24) - Forecast (17) = 7
- Week 4 Error: Actual (18) - Forecast (24) = -6
Step 3: Calculate the Bias
Bias can be calculated as the average of the forecast errors. Therefore, we first list the errors:
- Week 2 Error = 12
- Week 3 Error = 7
- Week 4 Error = -6
Now we will find the average of these errors:
\[ \text{Bias} = \frac{\text{Sum of Errors}}{\text{Number of Errors}} = \frac{(12 + 7 - 6)}{3} \]
\[ \text{Bias} = \frac{13}{3} \approx 4.33 \]
Conclusion
The bias calculated using the naïve forecast method is approximately 4.33. This indicates that, on average, the naïve forecast is under-forecasting the actual values.