Modeling Market Memory As Potential Indicators of Market Informational Efficiency

The purpose of this paper is to find a way of objectively benchmarking a selection of regional market against a relatively advanced market in the Asia Pacific in terms of their relative efficiency. Theoretically the Hurst Index ("H-Index") seems to be an appropriate absolute measure of the efficiency of a market as the Index purportedly reveals long run dependencies ("persistence") embedded in a candidate dataset. However, there have been some controversies about the various methodologies used in calculating the H-Index rendering the reliance on the H-Index as an absolute measure somewhat complicated and problematical. A large number of long range dependence estimators have been proposed from various research fields including physics, biology, engineering, and economics. Greene and Fielitz (1977) employed the classical Rescaled Range (R/S) analysis, first proposed by Hurst (1951). They analysed the daily returns of 200 common stocks listed in the New York Stock Exchange, and found that long-term dependence is a common characteristic amongst the sample stocks. Methods of determining long run dependence can be generally classified into two different domains: time domain based method and frequency domain based method. The time domain-based methods include Detrended Fluctuation Analysis (DFA) proposed by Peng et al (1994) and the Fractal Dimension method (Higuchi, 1988). The main advantages of the time domain based method are intuitive appeal, user friendliness and graphical visibility. On the other hand, the lack of a confidence interval and the necessity of Gaussian assumptions are some of the drawbacks. The absence of an analytic confidence interval makes it difficult to discriminate between small but statistically significant LRD from complete absence of LRD. Frequency domain-based methods include the Periodogram regression of Geweke and Porter-Hudak (1983), Wavelet estimator (Veitch and Abry, 1998), and Local Whittle estimator (Kunsh, 1987). Frequency domain methods are normally difficult to apply and to interpret, but they do provide an asymptotic distribution, hence provide a basis for conducting formal hypothesis test. There are merits in using H-Index as a relative measure of efficiency. We have chosen classical Hurst Rescaled Range Analysis (R/S Method) to derive the H-Index from the three methodologies including, Detrended Fluctuation Analysis (DFA) and semi-parametric GPH method. One of the reasons for the choice is the relative ease of implementation and its well understood algorithm. Further, since we are attempting to obtain a relative measure, most of the weaknesses that might emanate from using the R/S Method should, generally and mutually, be negated, when the different markets are compared. It is found that the use of the H-Index discriminates the lesser developed markets from the more developed ones. This is a first step in constructing an objective measure of relative efficiency of markets. If ongoing work proves this instrument to be robust, it can be adopted by international investors, fund managers and other interested parties to augment their respective decision making capabilities in assessing the relative efficiency, transparency, governance, and potential risks of their target markets.