Time-Series Model Evaluation with ARIMA

In the context of time-series analysis, consider the evaluation of a statistical model designed to forecast the monthly sales of a retail chain. The model used is an ARIMA (Autoregressive Integrated Moving Average) model, which was developed using historical sales data over the last five years. After fitting the model, the analyst conducts a backtesting procedure by comparing the forecasted sales against the actual sales over a recent 12-month period.

For model evaluation, the analyst uses several criteria, including Mean Absolute Error (MAE), Mean Squared Error (MSE), and the Akaike Information Criterion (AIC). While MAE and MSE measure the absolute and squared deviations of forecasted values from actual values, the AIC is used to assess the quality of the model relative to others by considering the goodness of fit and the number of parameters.

After evaluating the model, the analyst reports that the MAE is 200 units, the MSE is 60,000 units squared, and the AIC is -150. Based on these metrics, the analyst must determine which aspect of model evaluation they should focus on to justify maintaining the current ARIMA model or to consider an alternative model for future forecasts.