Nonparametric Prediction of Time Series on the Basis of Typical Course Patterns

Abstract

Long time series with high measurement frequencies (such as daily measurements) are often present in ecological studies. This holds true, for example, for pollution emissions in the air or for the run-off data of the Ruhr River analysed here. Parametric models, however, do not adequately deal with the frequently occurring nonlinear structures. The prediction techniques discussed in this article, which function on the basis of typical course patterns, are an alternative to parametric modelling. The predictions are averages of all time series data which have previous courses “similar” to the last known course. The methods differ only in the classification of those courses relevant to the forecast. The following three possibilities are presented for this: (i) The time series courses are divided into disjoined groups by means of nonhierarchical cluster analysis. (ii) Courses lying in a neighbourhood of the last known one form the forecast basis (kernel and nearest neighbour predictors). (iii) Such courses that after linear transformation lie near the last one and are positively correlated with it are included. The practical suitability of these methods will be tested on the basis of forecasts of the run-off of the Ruhr River. In this case the last method yields the best forecasts of the interesting peak data.