Evolutionary algorithms for the selection of time lags for time series forecasting by fuzzy inference systems

Time series forecasting by fuzzy inference systems based on optimal non-uniform attractor embedding in the multidimensional delay phase space is analyzed in this paper. A near-optimal set of time lags is identified by evolutionary algorithms after the optimal dimension of the reconstructed phase space is determined by the FNN (false nearest neighbors) algorithm. The fitness function is constructed in such a way that it represents the spreading of the attractor in the delay coordinate space but does not contain any information on prediction error metrics. The weighted one-point crossover rule enables an effective identification of near-optimal sets of non-uniform time lags which are better than the globally optimal set of uniform time lags. Thus the reconstructed information on the properties of the underlying dynamical system is directly elaborated in the fuzzy prediction system. A number of numerical experiments are used to test the functionality of this method.

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