Decomposition of time series by using the fractal signals based on the importance sampling and its applications

摘要

This report deals with the decomposition of time series by using the fractal signal based on the parameter estimation by the importance sampling. Assuming the models for generating the time series, the likelihood function is defined and the parameter are estimated based on the mean likelihood by using the Importance Sampling. The approximation in the wavelet coefficients is used for estimation as well as the relation defined for the variances of wavelet coefficients. The ability of the method is discussed for several cases of combination of fractal dimension and variances of the fractal time series. After completing the decomposition of underlying time series into several fractal time series, the prediction method for the fractal time series based on the scale expansion is employed.