Questions: For the following time series, you are given the moving average forecast. Time Period Time Series Value Moving Average Forecast --------- 1 23 2 17 3 17 4 26 19 5 11 20 6 23 18 7 17 20 The mean squared error equals a. 164 b. 0 c. 41 d. 6

Solution Steps

To calculate the mean squared error (MSE) for the given time series and moving average forecast, follow these steps:

1. Identify the time periods where both the actual time series values and the moving average forecasts are available.
2. For each of these periods, calculate the squared difference between the actual value and the forecasted value.
3. Sum all the squared differences.
4. Divide the sum by the number of periods to get the mean squared error.

The actual time series values and their corresponding moving average forecasts are as follows:

• Actual values: \( [26, 11, 23, 17] \)
• Forecasts: \( [19, 20, 18, 20] \)

We compute the squared differences between the actual values and the forecasts for each period: \[ \begin{align_} (26 - 19)^2 & = 49 \\ (11 - 20)^2 & = 81 \\ (23 - 18)^2 & = 25 \\ (17 - 20)^2 & = 9 \\ \end{align_} \] Thus, the squared differences are \( [49, 81, 25, 9] \).

The mean squared error is calculated by taking the average of the squared differences: \[ \text{MSE} = \frac{49 + 81 + 25 + 9}{4} = \frac{164}{4} = 41.0 \]

Final Answer