The Environmental Long-Memory Space-Time Series Prediction

Abstract

Temporal predictions by using long memory time series models have recently attracted much attention. In real surveys, such as those on environmental pollution, the observed data have long memory characteristics. In particular, the time series of pollution usually show “persistence†in the sense that their correlation functions decrease to zero at a much slower rate than the exponential rate implied by a short memory time series. In the literature, several contributions for the multistep prediction of univariate long memory time series have been proposed. However, in pollution studies, the phenomena are generally observed in several points of a study area so that a space-time series is available. In this context, we consider a multivariate extension of the univariate methodology in order to develop a multistep long memory space-time series prediction. For an easier evaluation of the procedure proposed, we focus our attention on bivariate long memory space-time series in ecological framework. The two proposed approaches of multistep prediction of the concentration of carbon monoxide in the Bergamo (Italy)-District are compared.

Keywords: AIC criterion, indirect inference, multistep prediction, VAR models, VARFI models