Memory effect in financial data : estimation and test

Abstract

In this thesis, I will use several statistics to detect long-range dependence in time series. I will begin the investigation with the Whittle method introduced by Whittle (1951) for random variables and the classical R/S method introduced by Mandelbrot and his coworkers in 1968, which was developed by Hurst (1951) in his studies of the Nile River discharges. Since the R/S statistic has strong preference towards longrange dependence, the most important shortcoming is its insensitivity to short-range dependence. Then, I will describe Lo’s method (1991), the modified R/S statistic, and use this method to overcome these shortcomings. In his method, Lo introduced the parameter q to construct S(q), the square root of a consistent estimator of partial sum’s variance, replaced S by this S(q). Then a problem comes out. The result of Lo’s method is asymptotic, but in practice, the sample size always be finite. Then I will discuss the ’right’ choice of the q, even this topic is still an open question now. After these, I am going to analyze the returns of the stock market by using these methods, hope to find if any evidence of long-range dependence in returns for stock market prices.