Ordinal time series model for forecasting air quality index for ozone in Southern California

Air quality index (AQI) for ozone is currently divided into six states depending on the level of public health concern. Generalized linear type modeling is a convenient and effective way to handle the AQI state, which can be characterized as non-stationary ordinal-valued time series. Various link functions which include cumulative logit, cumulative probit, and complimentary log-log are considered, and the partial maximum likelihood method is used for estimation. For a comparison purpose, the identity link, which yields a multiple regression model on the cumulative probabilities, is also considered. Random time-varying covariates include past AQI states, various meteorological processes, and periodic components. For model selection and comparison, the partial likelihood ratio tests, AIC and SIC are used. The proposed models are applied to 3 years of daily AQI ozone data from a station in San Bernardino County, CA. An independent year-long data from the same station are used to evaluate the performance of day-ahead forecasts of AQI state. The results show that the logit and probit models remove the non-stationarity in residuals, and both models successfully forecast day-ahead AQI states with almost 90 % of the chance.