Prediction of chaotic time series with wavelet coefficients

Using the wavelet transform, we can express a time series as a summation of frequency components each of which is localized in the frequency domain. In the present paper, we show that each frequency component given as the wavelet coefficients of a deterministic time series preserves the topological structure of the original dynamical system. We subsequently propose new methods to predict a time series by applying the inverse wavelet transform to predictees of frequency components. Our methods can realize good long-term predictions of deterministic time series contaminated with either high-frequency deterministic noise or white noise.