Accounting seasonal nonstationarity in time series models for short-term ozone level forecast

Due to the nonlinear feature of a ozone process, regression based models such as the autoregressive models with an exogenous vector process (ARX) suffer from persistent diurnal behaviors in residuals that cause systematic over-predictions and under-predictions and fail to make accurate multi-step forecasts. In this article we present a simple class of the functional coefficient ARX (FARX) model which allows the regression coefficients to vary as a function of another variable. As a special case of the FARX model, we investigate the threshold ARX (TARX) model of Tong [Lecture notes in Statistics, Springer-Verlag, Berlin, 1983; Nonlinear time series: a dynamics system approach, Oxford University Press, Oxford, 1990] which separates the ARX model in terms of a variable called the threshold variable. In this study we use time of day as the threshold variable. The TARX model can be used directly for ozone forecasts; however, investigation of the estimated coefficients over the threshold regimes suggests polynomial coefficient functions in the FARX model. This provides a parsimonious model without deteriorating the forecast performance and successfully captures the diurnal nonstationarity in ozone data. A general linear F-test is used to test varying coefficients and the portmanteau tests, based on the autocorrelation and partial autocorrelation of fitted residuals, are used to test error autocorrelations. The proposed models were applied to a 2 year dataset of hourly ozone concentrations obtained in downtown Cincinnati, OH, USA. For the exogenous processes, outdoor temperature, wind speed, and wind direction were used. The results showed that both TARX and FARX models substantially improve one-day-ahead forecasts and remove the diurnal pattern in residuals for the cases considered.