Forecasting methods for additive linear models with autoregressive symmetric errors

Additive linear models with autoregressive symmetric errors provide a flexible framework for modeling time series with trend and seasonality components, and autoregressive errors with heavier or lighter tails than the Gaussian ones. This paper introduces and evaluates a forecasting method for this class of models, as well as five methods to compute prediction intervals. Simulation studies are conducted to compare these five methods. Additionally, we illustrate the model estimation, diagnostics, and forecasting procedure, applying them to two time series: the annual global mean temperature anomaly and weekly respiratory hospitalizations in Costa Rica. A comparative study is performed against common forecasting methods (ARIMA, PROPHET, and a linear model). We demonstrate that our approach is competitive with these alternatives.