To calculate the bias using a naïve forecast, we first need to understand that a naïve forecast for the next period is simply the actual value from the previous period.
Here are the time series values for the given weeks:
- Week 1: 24
- Week 2: 16
- Week 3: 9
- Week 4: 14
Now, let's establish the naïve forecasts for each week, starting from Week 2 (since there's no prior week for Week 1):
- Forecast for Week 2 = Actual value of Week 1 = 24
- Forecast for Week 3 = Actual value of Week 2 = 16
- Forecast for Week 4 = Actual value of Week 3 = 9
Next, we can compare these forecasts with the actual values to calculate the forecast errors:
-
Week 2: Forecast = 24; Actual = 16
Error = 16 - 24 = -8 -
Week 3: Forecast = 16; Actual = 9
Error = 9 - 16 = -7 -
Week 4: Forecast = 9; Actual = 14
Error = 14 - 9 = 5
Now we have the forecast errors for each week:
- Week 2: -8
- Week 3: -7
- Week 4: 5
To calculate the bias, we sum the forecast errors and divide by the number of observations:
- Sum of the errors = -8 + (-7) + 5 = -10
- The number of forecasts (observations) = 3 (Week 2, Week 3, and Week 4)
Finally, calculate the bias:
\[ \text{Bias} = \frac{\text{Sum of Errors}}{\text{Number of Forecasts}} = \frac{-10}{3} \approx -3.33 \]
Thus, the bias based on the naïve forecast is approximately -3.33. This indicates that, on average, the naïve forecast is underestimating the actual values by about 3.33 units.