To calculate the bias using the naïve forecast method, we first need to understand what the naïve forecast method is. In this approach, the forecast for the next period is simply the actual value of the most recent period.
Actual Values:
- Week 1: 15
- Week 2: 14
- Week 3: 18
- Week 4: 13
Naïve Forecasts:
- Week 1: No forecast (no previous week)
- Week 2: Forecast = Week 1 value = 15
- Week 3: Forecast = Week 2 value = 14
- Week 4: Forecast = Week 3 value = 18
Calculated Forecasts:
- Week 2 Forecast = 15 (from Week 1)
- Week 3 Forecast = 14 (from Week 2)
- Week 4 Forecast = 18 (from Week 3)
Bias Calculation:
Bias is calculated as the average of the forecast errors, where the forecast error is the actual value minus the forecast for each week (excluding the first week).
\[ \text{Forecast Error} = \text{Actual Value} - \text{Forecast} \]
-
Week 2: Actual = 14, Forecast = 15
- Forecast Error = 14 - 15 = -1
-
Week 3: Actual = 18, Forecast = 14
- Forecast Error = 18 - 14 = 4
-
Week 4: Actual = 13, Forecast = 18
- Forecast Error = 13 - 18 = -5
Forecast Errors:
- Week 2: -1
- Week 3: 4
- Week 4: -5
Average Bias:
Now, we calculate the average of these forecast errors to find the bias.
\[ \text{Bias} = \frac{\text{Sum of Forecast Errors}}{\text{Number of Forecast Errors}} \]
Calculating the sum of the forecast errors: \[ \text{Sum} = -1 + 4 - 5 = -2 \]
Number of errors = 3.
Now, calculate the bias: \[ \text{Bias} = \frac{-2}{3} \approx -0.67 \]
Conclusion:
The bias using the naïve forecast method for the given time series data is approximately -0.67. This indicates a tendency to overestimate the actual values.