Forecasting on chaotic time series: A local optimal linear-reconstruction method

An alternative forecasting technique for chaotic time series, based on the optimal association concept, is presented. The method is applied on series generated by the logistic and H\'enon maps, and on experimental data corresponding to rainfall of a storm event. In all three cases the quality of the forecasts is analyzed in terms of the prediction interval, the length of the historic data available on the time series, and the dimension of the embedding space. It is shown that the method is capable of producing very satisfactory short-term forecasts for data sequences of small lengths as they often occur in real experiments. Our results also show that the present technique can be used to discriminate complex signals associated with deterministic chaos from those of random origin.