Research on similarity of stochastic non-stationary time series based on wavelet-fractal

Traditional dimension reduction methods lead to the disappearance of the important features of time series about non-linearity and fractal. The matching method based on wavelet transformation measures the similarity by using the distance standard at some resolution level. But in the case of an unknown fractal dimension of non-stationary time series, the local error of similarity matching of series increases. The process of querying the similarity of curve figures will be affected to a certain degree. Stochastic non-stationary time series show the non-linear and fractal characters in the process of time-space kinetics evolution. The concept of series fractal time-varying dimension is presented. The original Fractal Brownian Motion model is reconstructed to be a stochastic process with local self-similarity. An evaluation formula and algorithm of the time-varying Hurst index is established. A new determinant standard of series similarity is also introduced. Similarity of the basic curve figures is queried and measured at some resolution ratio level, in the meantime, the fractal dimension in local similarity is matched. The effectiveness of the method is validated by means of the simulation example.