A METHOD FOR PREDICTING CHAOTIC TIME-SERIES WITH OUTLIERS

In recent years, there have been intensive studies on the short-term, prediction method for time-series data with chaotic properties. The prediction for the chaotic time-series data is executed, for example, as follows. Based on the single-variable time-series data, the trajectory of the attractor is reconstructed in the multidimensional space and the change of the trajectory is predicted by a polynomial approximation. However, when there exists a noise such as the outlier in the time-series, the prediction error is increased drastically. To solve this problem, this paper proposes a prediction method which is robust against the outlier. More precisely, the following three elaborations are added to the conventional method: (1) the coefficients of the polynomial are calculated by Biweight's estimation method; (2) the order of the polynomial is determined automatically examining the residual error; and (3) the data with a large prediction error are replaced by the predicted value and the next prediction is applied. An evaluation experiment is executed for the data where the pseudorandom variable with the Cauchy distribution is superposed on the chaotic time-series data generated by the Henon map and the Lorenz model. It is verified as a result that the proposed method can well suppress the increase of the prediction error due to the outliers, improving greatly the accuracy of the prediction compared to the conventional method.