Modeling and forecasting daily maximum hourly ozone concentrations using the RegAR model with skewed and heavy-tailed innovations

Abstract

This paper considers the modeling and forecasting of daily maximum hourly ozone concentrations in Laranjeiras, Serra, Brazil, through dynamic regression models. In order to take into account the natural skewness and heavy-tailness of the data, a linear regression model with autoregressive errors and innovations following a member of the family of scale mixture of skew-normal distributions was considered. Pollutants and meteorological variables were considered as predictors, along with some deterministic factors, namely week-days and seasons. The Oceanic Nino Index was also considered as a predictor. The estimated model was able to explain satisfactorily well the correlation structure of the ozone time series. An out-of-sample forecast study was also performed. The skew-normal and skew-t models displayed quite competitive point forecasts compared to the similar model with gaussian innovations. On the other hand, in terms of forecast intervals, the skewed models presented much better performance with more accurate prediction intervals. These findings were empirically corroborated by a forecast Monte Carlo experiment.