R/S Analysis and Long Term Dependence in Stock Market Indices

Abstract

Recent studies indicating long term dependence in stock market indices have found a mean reversion process. However, studies using rescaled range (R/S) analysis have not found evidence of a mean reversion or ergodic process. Instead, evidence from these studies indicate either long term persistence in a nonperiodic cycle or short run Markovian dependence with no long term persistence. The purpose of this paper is to study the issue of long term dependence using rescaled range analysis. The empirical results obtained in this study support the persistent dependence/nonperiodic cycle results and suggest that the dependence arises from the general economic cycle.

The Efficient Market Hypothesis: Empirical Evidence

“…1, No. 2;2012 low or if the correlation across analysts' signals is high. Jaffe and Mahoney (1999) analysed the recommendations of common stocks made by the investment newsletters followed by the Hulbert Financial Digest.…”

“…Mills (1993) found little evidence of long memory in daily UK stock returns. Nawrocki (1995) considered the CRSP monthly value-weighted index and the S&P 500 daily index, and found that the Hurst exponent and the Lo-modified R/S statistic indicate that there is persistent finite memory. Chow et al (1996) found evidence that consistently revealed the absence of long-term dependence in 22 international equity market indices.…”

Using Wavelets for Compression and Detecting Events in Anomalous Network Traffic

“…However, the edge values of the sample region are not considered. This is because for the smallest samples, the R/S values are biased due to shortrange correlations; whereas for the largest samples the R/S values are statistically insignificant [16], [14]. The slope of the regression line is an estimate of the Hurst parameter [15], [14].…”

“…Estimating the Long Range Dependence 1) The Rescaled Adjusted Range Statistic: For the estimation of the Hurst parameter an algorithm was developed based on the rescaled range (R/S) statistic. The R/S statistic is the range of partial sums of deviations of a time series from its mean, rescaled by its standard deviation [14].…”

Applying wavelets for the controlled compression of communication network measurements

“…For the regression analysis the edge values should not be considered [30], [36]. Thus, in order to exclude the edge values, a window that includes 90% of the data trace values was utilized.…”