Relationship between degree of efficiency and prediction in stock price changes

This study investigates empirically whether the degree of stock market efficiency is related to the prediction power of future price change using the indices of twenty seven stock markets. Efficiency refers to weak-form efficient market hypothesis (EMH) in terms of the information of past price changes. The prediction power corresponds to the hit-rate, which is the rate of the consistency between the direction of actual price change and that of predicted one, calculated by the nearest neighbor prediction method (NN method) using the out-of-sample. In this manuscript, the Hurst exponent and the approximate entropy (ApEn) are used as the quantitative measurements of the degree of efficiency. The relationship between the Hurst exponent, reflecting the various time correlation property, and the ApEn value, reflecting the randomness in the time series, shows negative correlation. However, the average prediction power on the direction of future price change has the strongly positive correlation with the Hurst exponent, and the negative correlation with the ApEn. Therefore, the market index with less market efficiency has higher prediction power for future price change than one with higher market efficiency when we analyze the market using the past price change pattern. Furthermore, we show that the Hurst exponent, a measurement of the long-term memory property, provides more significant information in terms of prediction of future price changes than the ApEn and the NN method.Comment: 10 page

Market Efficiency in Foreign Exchange Markets

We investigate the relative market efficiency in financial market data, using the approximate entropy(ApEn) method for a quantification of randomness in time series. We used the global foreign exchange market indices for 17 countries during two periods from 1984 to 1998 and from 1999 to 2004 in order to study the efficiency of various foreign exchange markets around the market crisis. We found that on average, the ApEn values for European and North American foreign exchange markets are larger than those for African and Asian ones except Japan. We also found that the ApEn for Asian markets increase significantly after the Asian currency crisis. Our results suggest that the markets with a larger liquidity such as European and North American foreign exchange markets have a higher market efficiency than those with a smaller liquidity such as the African and Asian ones except Japan

Heterogeneous Agents Models: two simple examples, forthcoming In: Lines, M. (ed.) Nonlinear Dynamical Systems in Economics, CISM Courses and Lectures, Springer, 2005, pp.131-164.

These notes review two simple heterogeneous agent models in economics and finance. The first is a cobweb model with rational versus naive agents introduced in Brock and Hommes (1997). The second is an asset pricing model with fundamentalists versus technical traders introduced in Brock and Hommes (1998). Agents are boundedly rational and switch between different trading strategies, based upon an evolutionary fitness measure given by realized past profits. Evolutionary switching creates a nonlinearity in the dynamics. Rational routes to randomness, that is, bifurcation routes to complicated dynamical behaviour occur when agents become more sensitive to differences in evolutionary fitness.

Grasping asymmetric information in market impacts

The price impact for a single trade is estimated by the immediate response on an event time scale, i.e., the immediate change of midpoint prices before and after a trade. We work out the price impacts across a correlated financial market. We quantify the asymmetries of the distributions and of the market structures of cross-impacts, and find that the impacts across the market are asymmetric and non-random. Using spectral statistics and Shannon entropy, we visualize the asymmetric information in price impacts. Also, we introduce an entropy of impacts to estimate the randomness between stocks. We show that the useful information is encoded in the impacts corresponding to small entropy. The stocks with large number of trades are more likely to impact others, while the less traded stocks have higher probability to be impacted by others

Multi-Fractal Spectral Analysis of the 1987 Stock Market Crash

The multifractal model of asset returns captures the volatility persistence of many financial time series. Its multifractal spectrum computed from wavelet modulus maxima lines provides the spectrum of irregularities in the distribution of market returns over time and thereby of the kind of uncertainty or randomness in a particular market. Changes in this multifractal spectrum display distinctive patterns around substantial market crashes or drawdowns. In other words, the kinds of singularities and the kinds of irregularity change in a distinct fashion in the periods immediately preceding and following major market drawdowns. This paper focuses on these identifiable multifractal spectral patterns surrounding the stock market crash of 1987. Although we are not able to find a uniquely identifiable irregularity pattern within the same market preceding different crashes at different times, we do find the same uniquely identifiable pattern in various stock markets experiencing the same crash at the same time. Moreover, our results suggest that all such crashes are preceded by a gradual increase in the weighted average of the values of the Lipschitz regularity exponents, under low dispersion of the multifractal spectrum. At a crash, this weighted average irregularity value drops to a much lower value, while the dispersion of the spectrum of Lipschitz exponents jumps up to a much higher level after the crash. Our most striking result, therefore, is that the multifractal spectra of stock market returns are not stationary. Also, while the stock market returns show a global Hurst exponent of slight persistence 0.5Financial Markets, Persistence, Multi-Fractal Spectral Analysis, Wavelets