Research And Application Of Time-varying Hurst Parameter Estimation Methods For Time Series Of Self-similarity

In reality,most of random signal sequences are non-stationary,some of them have obvious characteristics of self-similarity.Self-similarity reflects the correlation between the local and the whole signal,which can be described by Hurst parameters.The traditional Hurst parameter is a global index,that is,the Hurst parameter of the whole signal is a constant,which represents self-similar characteristics of the whole signal.However,in the process of analyzing the self-similarity of some long-term data,experts and scholars have found that Hurst parameters are different in different periods.The traditional Hurst parameter estimation methods only reflect the self-similarity of the whole data,and its estimation results can not describe the local mutational information of these signals.Therefore,the analysis of the local self-similarity of data has been paid more and more attention.It is of great significance to study and analyze the local self-similarity of time series data for establishing more accurate system model and data prediction.This thesis first introduces the definition and related theory of self-similar time series,and then introduces the fractal Brownian motion model and the fractal Gauss noise model.In this thesis,the traditional Hurst parameter estimation methods are used to deeply study the time-varying Hurst parameter estimation,and get the more accurate estimation result.In this thesis,two improved methods are used to analyze the local Hurst parameters with self-similarity,and the improved methods are designed and realised by using MATLAB simulation software.Firstly,to study the local characteristics of random sequence,the time-varying Hurst parameters are estimated based on the sliding window function.Secondly,the weighted average method is introduced to estimate the time-varying Hurst parameters,and exponential smoothing is used in the moving time window to dynamically study the sequence of self-similarity.In addition,in order to verify the reliability of the improved Hurst parameter estimation methods in this study,the improved methods in this thesis is applied to the analysis of actual network traffic,which provides an effective method for complex time-varying data analysis.