Improvement And Application Of Hurst Parameter Estimation Method For Time Series With Long-range Dependence

In the real world,many random signals have long-range dependence or local-range dependence,such as the train vibration signal,bearing fault signals.There are some signals which not only has long-range dependence,but also has peak and heavy tailed distribution characteristics,such as financial data,network data and various biological signal data.These signals are subject to non-Gauss distribution,and they belong to the non-Gauss signal.However,the emergence of long-range dependence and heavy tailed distribution brings difficulties to the analysis of signal.The important parameter that describes the time series with long-range dependence is Hurst parameter.Some estimation methods are proposed for Hurst parameters,such as R/S method,periodogram method and absolute value method,etc..From the theory,these Hurst parameter estimation methods can estimate Hurst parameters of the time series with long-range dependence.But in real life,different Hurst parameter estimation methods have large differences.So conducting an in-depth understanding for the nature and function of the Hurst parameter estimation methods and modifying it are needed.It is of great significance to improve the Hurst parameter estimation methods for the analysis of financial data,network traffic monitoring and other practical problems.In this thesis,firstly some related definitions and theories about the long correlation process are introduced.Then some common long correlation models are introduced.Eight common Hurst parameter estimation methods for time series with long-range dependence are assessed in the effect of heavy tailed distribution.According to the evaluation results,the robustness and high accuracy of residual variance method,periodogram method and Higuchi method are higher.The three reliable Hurst parameter estimation methods are modified.Sliding window method is used to estimate the Hurst parameters.Based on sliding window analysis method,Rectangular window,Hamming window,Hanning window,Gauss window and Blackman window are combined with Hurst parameter estimation methods to get more flexible and accurate estimation methods.The five sliding windows are added to the three Hurst parameter estimation methods based on improving the accuracy of Hurst parameter estimation methods,and the Hurst parameter estimation is realized by using Matlab.In addition,in order to prove the reliability of the modified Hurst parameter estimation methods in this study,they are applied to the analysis of financial data and other related real time series.And it is proved that the modified Hurst parameter estimation methods are effective.