Long-term memory of the returns in the Chinese stock indices

Abstract

The modified R/S statistic (MRS) and the local Whittle method (LWM) are used to analyze the long-range dependence on various indices of the Chinese stock markets. The MRS accepts the null hypothesis of no long-range dependence while the LWM rejects it. We also find that the long-range dependence phenomena presented in these markets depend on the time in which they are measured. Keywords long-range dependence, modified R/S statistic, local Whittle estimator PACS numbers 89.65.Gh, 05.45.Tp, 02.50.-r ½ ÁÒØÖÓ Ù Ø ÓÒLong-range dependence, also commonly referred to as long-term memory or correlation, has a long history and remains an active topic of research in the study of financial time series. A lot of empirical studies have been done on the long-range dependence of stock markets. In 1970s Mandelbrot [1−3] introduced the rescaled range statistic (R/S) method, which was originally invented by Hurst [4], to evaluate the Hurst exponent H in analyzing the long-term memory of security returns, and found that it was quite larger than 1/2 for stock prices and returns of interest rates. It displays a strong positive long-range correlation, and challenges the efficient market hypothesis and the related random walk model. A clear description of these issues can be found in Ref. [5]. Similar results were also obtained by Greene and Fielitz [6]. As we know, many other financial variables (such as volatility, trade sign, et al.) possess long-term memory, which are less debated. However, there is a tremendous discord between affirmation and denial of the long-term memory for security returns. In 1988 Fama and French [7] argued that the long-range dependence of stock returns is weak for weekly and daily data, and returns for a longer time have a negative correlation. Aydogan and Booth [8] believed that no long-term dependence exists in stock returns. In 1991 Lo [9] declared that the classical R/S analysis is sensitive to the presence of short-range dependencies. Evidence of dependence using the classical R/S statistic may come merely from short-range dependencies instead of long-range ones. He proposed a modified R/S (MRS) statistic to determine the long-term memory. Nevertheless, some economists said that an acceptance of the null hypothesis of no long-range dependence based on the MRS statistic should never be viewed as the "final word". Teverovsky, Taqqu and Willinger [10] identified a number of problems associated with Lo's method and its use in practice. They verified that Lo's MRS statistic has a strong preference for accepting the null hypothesis of no long-range dependence.Another widely used methodology, called the Whittle estimator, evaluates the long-term memory parameter through the log-periodogram regression estimator proposed by Geweke and Porter-Hudak [11]. Unlike the MRS, this method is frequency-domain based and applies maximum likelihood techniques. However, it has been criticized because of its finite-sample bias. Robinson [12] proposed a least biased semi-parametric estima-

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