Recursive modelling and adaptive forecasting of air quality data

Abstract

Recursive methods of time series analysis developed in recent years provide a natural approach to the estimation of models with time-variable parameters, and hence a useful tool for the study of environmental data. This paper presents a fully recursive approach to the modelling and adaptive forecasting of non-stationary air quality time series. The approach is based on time-variable parameter versions of various well-known time series models and exploits the suite of novel, recursive algorithms of the Kalman Filter. The observed series is decomposed into a simple additive `component' with each component model written in the state-space Gauss-Markov form, in which the model parameter variations are assumed to follow a `generalized random walk' process. The flexibility of this stochastic formulation allows for a suitable degree of variability in the estimated components. For instance, it is possible to allows easily for discontinuities, missing data and outliers. The practical utility of this methodology is demonstrated by applying it to the modelling and forecasting of a set of air quality data obtained in 1996 from Hong Kong.