Predictive clustering on non-successive observations for multi-step ahead chaotic time series prediction

Predictive clustering algorithm based upon modified Wishart clustering technique is applied to predict chaotic time series. Concept of predictable and non-predictable observations is introduced in order to distinguish between reliable and unreliable predictions and, consequently, to enhance an ability to predict up to considerable number of positions ahead. Non-predictable observations are easily ascertained in the frameworks of predictive clustering, regardless used clustering technique. Clustering vectors are composed from observations according to set of patterns of non-successive positions in order to reveal characteristic observations sequences, useful for multi-step ahead predictions. The employed clustering method is featured with an ability to generate just enough clusters (submodels) to cope with inherent complexity of the series in question. The methods demonstrate good prediction quality for Lorenz system time series and satisfactory results for weather, energy market and financial time series.