Prediction of multivariate chaotic time series with local polynomial fitting

To improve the prediction accuracy of complex multivariate chaotic time series, a novel scheme formed on the basis of multivariate local polynomial fitting with the optimal kernel function is proposed. According to Takens Theorem, a chaotic time series is reconstructed into vector data, multivariate local polynomial regression is used to fit the predicted complex chaotic system, then the regression model parameters with the least squares method based on embedding dimensions are estimated,and the prediction value is calculated. To evaluate the results, the proposed multivariate chaotic time series predictor based on multivariate local polynomial model is compared with a univariate predictor with the same numerical data. The simulation results obtained by the Lorenz system show that the prediction mean squares error of the multivariate predictor is much smaller than the univariate one, and is much better than the existing three methods. Even if the last half of the training data are used in the multivariate predictor, the prediction mean squares error is smaller than that of the univariate predictor.