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. I n the present paper, we Show that each frequency component given as the wav elet coefficients of a deterministic time series preserves the topological structure of the original dynamical system. We subsequently propose new met hods 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-fre quency deterministic noise or white noise. (C) 2001 Scripta Technica.