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

At present, the similarity pattern query about time series is the research hotspot in knowledge discovering in the time series database. Traditional dimension reduction methods about similarity query introduce the smoothness to data series in some degree that the important features of time series about non-linearity and fractal are destroyed. The matching method based on wavelet transformation measures the similarity by using the distance standard at some resolution level. But in the case of unknowing the fractal dimension of non-stationary time series, the local error of similarity matching of series increases. The process of querying the similarity of curve figure 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 varying-time dimension is presented. The original fractal Brownian motion model is reconstructed to be a stochastic process with local self-similarity. The Daubechies wavelet is used to transform the local self-similarity process. An evaluation formula of varying-time Hurst index is established. The algorithm of varying-time index is presented. A new standard of series similarity is also introduced. The similarity of curve basic figure 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 in the end. The work of this paper is the supplement and development of the study on similarity mentioned in the literatures.