Hurst exponent and prediction based on weak-form efficient market hypothesis of stock markets

arXiv:0712.1624v1 [q-fin.ST] 11 Dec 2007 Hurst exponent and prediction based on weak-form efficient market hypothesis of stock markets Cheoljun Eom and Sunghoon Choi Division of Business Administration, Pusan National University, Busan 609-735, Republic of Korea Gabjin Oh NCSL, Department of Physics, Pohang University of Science and Technology, Pohang, Gyeongbuk, 790-784, Republic of Korea & Asia Pacific Center for Theoretical Physics, Pohang, Gyeongbuk, 790-784, Republic of Korea Woo-Sung Jung Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA (Dated: November 26, 2024) Abstract We empirically investigated the relationships between the degree of efficiency and the predictabil- ity in financial time-series data. The Hurst exponent was used as the measurement of the degree of efficiency, and the hit rate calculated from the nearest-neighbor prediction method was used for the prediction of the directions of future price changes. We used 60 market indexes of various countries. We empirically discovered that the relationship between the degree of efficiency (the Hurst exponent) and the predictability (the hit rate) is strongly positive. That is, a market index with a higher Hurst exponent tends to have a higher hit rate. These results suggested that the Hurst exponent is useful for predicting future price changes. Furthermore, we also discovered that the Hurst exponent and the hit rate are useful as standards that can distinguish emerging capital markets from mature capital markets. PACS numbers: 89.65.Gh,89.75.-k,89.75.Hc 1 I. INTRODUCTION In the field of finance, the efficient market hypothesis (EMH) proposed by Fama has had a great influence on theory and practice [1]. The EMH is based on whether newly generated information is instantaneously and sufficiently reflected in stock prices. Based on the point of time of generation, information can be classified into three types: historical information, public information, and future (or internal) information. Depending on the reflection of each information in stock prices, the EMH can be divided into three types: weak-form EMH of historical information, semi strong-form EMH of public information and strong-form EMH of future information. Recent research in the field of econophysics examining properties and phenomena of financial time-series through interdisciplinary studies are mostly related to weak-form EMH. The fact that weak-form EMH is supported by financial time-series means that historical information such as similar price change patterns is not useful for predicting future price changes. On the other hand, the fact that weak-form EMH is not supported means that similar price change patterns in the past have information values useful for predicting future price changes. Of the interdisciplinary studies in the fields of finance and econophysics, research on long- term memory properties have been of particular interest [2, 3, 4, 5, 6, 7]. Many researchers are interested in this research topic because the results of the existence of long-term memory properties not only serves as negative evidence of weak-form EMH but also is closely related to the predictability of stock prices. The Hurst exponent has been widely used as a method to measure long-term memory properties [8, 9, 10, 11, 12]. This measurement quantifies the degree of persistence of similar price change patterns, and it is closely related to weak-form EMH. Also, there are studies that have proposed that the Hurst exponent could be used as an efficiency measurement of stock markets [13, 14]. However, it is difficult to find studies that have empirically observed the relationship be- tween the existence of long-term memory properties and the predictability of future prices. To investigate such research, it is necessary to establish a prediction model which can ex- amine the practical relationship with the Hurst exponent, which represents a quantitative measurement of the degree of efficiency. Such a prediction model should be based on the use of similar price change patterns, which are common components between weak-form EMH and the Hurst exponent. Accordingly, we used the nearest-neighbor prediction (NN) 2 method, which uses similar price change patterns of the past for the prediction of future price changes [15, 16, 17, 18]. This method first sets the past price changes of a specific time period from the previous date, t, of a future trading date, t+1, to be predicted as the target price change pattern. Next, it selects a price change pattern of the past period similar to the target price change pattern. Finally, in order to predict the price of the future trading date, it uses the price change information generated by following the date of the selected price change pattern of the past. This NN method is known to be useful for short-term prediction. Accordingly, we empirically investigated the relationship between the predictability cal- culated from the NN method and the degree of efficie

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