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The Estimate Of Hurst Exponent In The Finance Market

Posted on:2011-04-08Degree:MasterType:Thesis
Country:ChinaCandidate:J P YeFull Text:PDF
GTID:2189360305477934Subject:Probability theory and mathematical statistics
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The long memory of time series array firstly was found by Hurst in 1951, and thenwas established mathematical foundation by introducing fraction Bromnian movement andconception of fractal by Mandelbrot.In the recent 20 years. Rearch on long memory has beenexpanded to the domain of economics and finance from natural science field.Especially,longmemory of financial time series array becomes a focus of study at home and broad. Thetraditional theory of capital markets in the normal distribution assumpts that price movementmeets the randomicity, but the fact is not the case. It is very important to analysis the longmemory of stock market.There are amount of papers at home and abroad to estimate Hurst index. Initially thereare the classic R/S estimates, the modified R / S estimates, Re?ective analysis, detrended?uctuation analysis (DFA), periodic regression (GPH), moving average, wavelet coefficient,multiscale estimation,and so on. This article describes the R/S estimates and multi-scaleestimates. We've found that the R/S estimates have shorcomings in shor-term memory bynumerical simulation. Based on these shortcomings, we use the multiscale to estimate Hurstindex. We've also found that multi-scale's calculation is faster than R/S , the deviation islittle and the estimated result is more accurate.This paper divide into five chapters, chapter 1 review the research background and practi-cal significance; Chapter 2 simulate fractional Brownian motion, and definite of Hurst index;the third chapter of paper introduce the R / S estimation and multi-scale estimation; In chap-ter 4 of this article, the 29 financial sector stocks of Shanghai Stock Exchange A share andthe RMB exchange the other 17 countries are taken as subjects, we do Hurst index for thedetailed analysis and estimation at four stock of Guo Jin , Xin Nan, Hua Xia and Tai Ping.The Hurst index values are greater than 0.5, which China's capital market shows the timeseries is fractal. Further research illustrates the stock market and foreign exchange market,high H value means low risk. Because the high H value means less noise, greater durabilityand more clearly the trend. Chapter 5 is the conclusion and outlook.
Keywords/Search Tags:Hurst Index, R/S Estimator, Scaling Estimator, Fraction Brownian motion, return of rate
PDF Full Text Request
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