Evaluation of ARIMA Model Performance

Hard Time-series Analysis Model Evaluation

During a recent analysis of quarterly sales data for a retail company, a finance team employed an autoregressive integrated moving average (ARIMA) model to forecast future sales. After estimating the model parameters and generating out-of-sample forecasts, they calculated the Mean Absolute Error (MAE) and the Root Mean Squared Error (RMSE) to evaluate the accuracy of their predictions.

Given that MAE is defined as:

$$ MAE =\frac{1}{n} imes ext{sum}(| ext{Actual} - ext{Forecast}|) $$

and RMSE is defined as:

$$ RMSE =\frac{1}{n} imes ext{sqrt}( ext{sum}(( ext{Actual} - ext{Forecast})^2)) $$

If the finance team reported an MAE of 100 and an RMSE of 200, which of the following statements regarding the evaluation of their ARIMA model is correct?

The RMSE is always lower than the MAE for the same data set.

The MAE provides a better assessment of model performance than the RMSE when there are outliers in the data.

The RMSE being higher than the MAE indicates that the forecast errors are normally distributed.

Hint

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