Relationship between efficiency and predictability in stock price change

In this study, we evaluate the relationship between efficiency and predictability in the stock market. The efficiency, which is the issue addressed by the weak-form efficient market hypothesis, is calculated using the Hurst exponent and the approximate entropy (ApEn). The predictability corresponds to the hit-rate; this is the rate of consistency between the direction of the actual price change and that of the predicted price change, as calculated via the nearest neighbor prediction method. We determine that the Hurst exponent and the ApEn value are negatively correlated. However, predictability is positively correlated with the Hurst exponent.     

Correlations in financial time series: established versus emerging markets

Long-time correlations in both well-developed and emerging market indexes are studied. The Hurst exponent as well as detrended fluctuations analysis (DFA) are used as technical tools. Some features that seem to be specific for developing markets are discovered and briefly discussed. Received 17 October 2000     

Inefficiency in Latin-American market indices

We explore the deviations from efficiency in the returns and volatility returns of Latin-American market indices. Two different approaches are considered. The dynamics of the Hurst exponent is obtained via a wavelet rolling sample approach, quantifying the degree of long memory exhibited by the stock market indices under analysis. On the other hand, the Tsallis q entropic index is measured in order to take into account the deviations from the Gaussian hypothesis. Different dynamic rankings of inefficieny are obtained, each of them contemplates a different source of inefficiency. Comparing with the results obtained for a developed country (US), we confirm a similar degree of long-range dependence for our emerging markets. Moreover, we show that the inefficiency in the Latin-American countries comes principally from the non-Gaussian form of the probability distributions.     

How fast do stock prices adjust to market efficiency? Evidence from a detrended fluctuation analysis

In this paper we analyse price fluctuations with the aim of measuring how long the market takes to adjust prices to weak-form efficiency, i.e., how long it takes for prices to adjust to a fractional Brownian motion with a Hurst exponent of 0.5. The Hurst exponent is estimated for different time horizons using detrended fluctuation analysis–a method suitable for non-stationary series with trends–in order to identify at which time scale the Hurst exponent is consistent with the efficient market hypothesis. Using high-frequency share price, exchange rate and stock data, we show how price dynamics exhibited important deviations from efficiency for time periods of up to 15 min; thereafter, price dynamics was consistent with a geometric Brownian motion. The intraday behaviour of the series also indicated that price dynamics at trade opening and close was hardly consistent with efficiency, which would enable investors to exploit price deviations from fundamental values. This result is consistent with intraday volume, volatility and transaction time duration patterns.     

Degree distributions of the visibility graphs mapped from fractional Brownian motions and multifractal random walks

The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian motions and multifractal random walks, and find that the degree distributions exhibit power-law behaviors, in which the power-law exponent α is a linear function of the Hurst index H of the time series. We also find that the degree distribution of the visibility graph is mainly determined by the temporal correlation of the original time series with minor influence from the possible multifractal nature. As an example, we study the visibility graphs constructed from three Chinese stock market indexes and unveil that the degree distributions have power-law tails, where the tail exponents of the visibility graphs and the Hurst indexes of the indexes are close to the α∼H linear relationship.     

Some comments on Hurst exponent and the long memory processes on capital markets

The analysis of long memory processes in capital markets has been one of the topics in finance, since the existence of the market memory could implicate the rejection of an efficient market hypothesis. The study of these processes in finance is realized through Hurst exponent and the most classical method applied is R/S analysis. In this paper we will discuss the efficiency of this methodology as well as some of its more important modifications to detect the long memory. We also propose the application of a classical geometrical method with short modifications and we compare both approaches.     

The grounds for time dependent market potentials from dealers’ dynamics

We apply the potential force estimation method to artificial time series of market price produced by a deterministic dealer model. We find that dealers’ feedback of linear prediction of market price based on the latest mean price changes plays the central role in the market’s potential force. When markets are dominated by dealers with positive feedback the resulting potential force is repulsive, while the effect of negative feedback enhances the attractive potential force.     

Endogenous and exogenous dynamics in the fluctuations of capital fluxes

A phenomenological investigation of the endogenous and exogenous dynamics in the fluctuations of capital fluxes is carried out on the Chinese stock market using mean-variance analysis, fluctuation analysis, and their generalizations to higher orders. Non-universal dynamics have been found not only in the scaling exponent α, which is different from the universal values 1/2 and 1, but also in the distributions of the ratio η= σ^exo / σ^endo of individual stocks. Both the scaling exponent α of fluctuations and the Hurst exponent H_i increase in logarithmic form with the time scale Δt and the mean traded value per minute 〈f_i 〉, respectively. We find that the scaling exponent α^endo of the endogenous fluctuations is independent of the time scale. Multiscaling and multifractal features are observed in the data as well. However, the inhomogeneous impact model is not verified.     

Visibility graph approach to exchange rate series

By means of a visibility graph, we investigate six important exchange rate series. It is found that the series convert into scale-free and hierarchically structured networks. The relationship between the scaling exponents of the degree distributions and the Hurst exponents obeys the analytical prediction for fractal Brownian motions. The visibility graph can be used to obtain reliable values of Hurst exponents of the series. The characteristics are explained by using the multifractal structures of the series. The exchange rate of EURO to Japanese Yen is widely used to evaluate risk and to estimate trends in speculative investments. Interestingly, the hierarchies of the visibility graphs for the exchange rate series of these two currencies are significantly weak compared with that of the other series.     

Roughness and finite size effect in the NYSE stock-price fluctuations

We consider the roughness properties of NYSE (New York Stock Exchange) stock-price fluctuations. The statistical properties of the data are relatively homogeneous within the same day but the large jumps between different days prevent the extension of the analysis to large times. This leads to intrinsic finite size effects which alter the apparent Hurst (H) exponent. We show, by analytical methods, that finite size effects always lead to an enhancement of H. We then consider the effect of fat tails on the analysis of the roughness and show that the finite size effects are strongly enhanced by the fat tails. The non stationarity of the stock price dynamics also enhances the finite size effects which, in principle, can become important even in the asymptotic regime. We then compute the Hurst exponent for a set of stocks of the NYSE and argue that the interpretation of the value of H is highly ambiguous in view of the above results. Finally we propose an alternative determination of the roughness in terms of the fluctuations from moving averages with variable characteristic times. This permits to eliminate most of the previous problems and to characterize the roughness in useful way. In particular this approach corresponds to the automatic elimination of trends at any scale.     

Generalized Hurst exponent approach to efficiency in MENA markets

We study the time-varying efficiency of 15 Middle East and North African (MENA) stock markets by generalized Hurst exponent analysis of daily data with a rolling window technique. The study covers a time period of six years from January 2007 to December 2012. The results reveal that all MENA stock markets exhibit different degrees of long-range dependence varying over time and that the Arab Spring has had a negative effect on market efficiency in the region. The least inefficient market is found to be Turkey, followed by Israel, while the most inefficient markets are Iran, Tunisia, and UAE. Turkey and Israel show characteristics of developed financial markets. Reasons and implications are discussed.     

The use of the Hurst exponent to predict changes in trends on the Warsaw Stock Exchange

The local properties of the time series of the evolution of share prices of 126 significant companies traded on the Warsaw Stock Exchange during the period between 1991-2008 have been investigated. The analysis was applied to daily financial returns. I have used the local DFA to obtain the Hurst exponent (diffusion coefficient) while searching for negative correlations by which changes of long-term trends would be effected. A certain evidence, proving that after the signature of anti-correlation-the drop in the Hurst exponent-the change in the trend and in the return rate of an investment is probable, was pointed out. Hence after further investigation this method may be useful as a part of an investment strategy. As the Warsaw Stock Exchange is relatively smaller and younger than other significant world Stock Exchanges-and as the developing market is less efficient-the generalization for others markets needs further investigation.     

Micro-economic analysis of the physical constrained markets: game theory application to competitive electricity markets

Competition has been introduced in the electricity markets with the goal of reducing prices and improving efficiency. The basic idea which stays behind this choice is that, in competitive markets, a greater quantity of the good is exchanged at a lower price, leading to higher market efficiency. Electricity markets are pretty different from other commodities mainly due to the physical constraints related to the network structure that may impact the market performance. The network structure of the system on which the economic transactions need to be undertaken poses strict physical and operational constraints. Strategic interactions among producers that game the market with the objective of maximizing their producer surplus must be taken into account when modeling competitive electricity markets. The physical constraints, specific of the electricity markets, provide additional opportunity of gaming to the market players. Game theory provides a tool to model such a context. This paper discussed the application of game theory to physical constrained electricity markets with the goal of providing tools for assessing the market performance and pinpointing the critical network constraints that may impact the market efficiency. The basic models of game theory specifically designed to represent the electricity markets will be presented. IEEE30 bus test system of the constrained electricity market will be discussed to show the network impacts on the market performances in presence of strategic bidding behavior of the producers.     

Nonlinear bivariate dependency of price-volume relationships in agricultural commodity futures markets: A perspective from Multifractal Detrended Cross-Correlation Analysis

Nonlinear dependency between characteristic financial and commodity market quantities (variables) is crucially important, especially between trading volume and market price. Studies on nonlinear dependency between price and volume can provide practical insights into market trading characteristics, as well as the theoretical understanding of market dynamics. Actually, nonlinear dependency and its underlying dynamical mechanisms between price and volume can help researchers and technical analysts in understanding the market dynamics by integrating the market variables, instead of investigating them in the current literature. Therefore, for investigating nonlinear dependency of price-volume relationships in agricultural commodity futures markets in China and the US, we perform a new statistical test to detect cross-correlations and apply a new methodology called Multifractal Detrended Cross-Correlation Analysis (MF-DCCA), which is an efficient algorithm to analyze two spatially or temporally correlated time series. We discuss theoretically the relationship between the bivariate cross-correlation exponent and the generalized Hurst exponents for time series of respective variables. We also perform an empirical study and find that there exists a power-law cross-correlation between them, and that multifractal features are significant in all the analyzed agricultural commodity futures markets.     

Time series analysis and long range correlations of Nordic spot electricity market data

The electricity system price of the Nord Pool spot market is analysed. Different time scale analysis tools are assessed with focus on the Hurst exponent and long range correlations. Daily and weekly periodicities of the spot market are identified. Even though space time separation plots suggest more stationary behaviour than other financial time series, we find large fluctuations of the spot price market which suggest time-dependent scaling parameters.     

Unified index to quantifying heterogeneity of complex networks

Although recent studies have revealed that degree heterogeneity of a complex network has significant impact on the network performance and function, a unified definition of the heterogeneity of a network with any degree distribution is absent. In this paper, we define a heterogeneity index 0≤H<1 to quantify the degree heterogeneity of any given network. We analytically show the existence of an upper bound of H=0.5 for exponential networks, thus explain why exponential networks are homogeneous. On the other hand, we also analytically show that the heterogeneity index of an infinite power law network is between 1 and 0.5 if and only if its degree exponent is between 2 and 2.5. We further show that for any power law network with a degree exponent greater than 2.5, there always exists an exponential network such that both networks have the same heterogeneity index. This may help to explain why 2.5 is a critical degree exponent for some dynamic behaviors on power law networks.     

Time and scale Hurst exponent analysis for financial markets

We use a new method of studying the Hurst exponent with time and scale dependency. This new approach allows us to recover the major events affecting worldwide markets (such as the September 11th terrorist attack) and analyze the way those effects propagate through the different scales. The time-scale dependence of the referred measures demonstrates the relevance of entropy measures in distinguishing the several characteristics of market indices: “effects” include early awareness, patterns of evolution as well as comparative behaviour distinctions in emergent/established markets.     

A Monte Carlo simulation to the performance of the R/S and V/S methods—Statistical revisit and real world application

A correct or precise estimation of the Hurst exponent is one of the fundamentally important problems in the financial economics literature. There are three widely used tools to estimate the Hurst exponent, the canonical rescaled range (R/S), the variance rescaled statistic (V/S) and the Modified rescaled range (Modified R/S). To clarify their performance, we compare them by Monte Carlo simulations; we generate many time-series of a fractal Brownian motion, of a Weierstrass–Mandelbrot cosine fractal function and of a fractionally integrated process, whose theoretical Hurst exponents are known, to compare the Hurst exponents estimated by the three methods. To better understand their pragmatic performance, we further apply all of these methods empirically in real-world applications. Our results imply it is not appropriate to conclude simply which method is better as V/S performs better when the analyzed market is anti-persistent while R/S seems to be a reliable tool used in persistent market.     

Feedback and efficiency in limit order markets

A consistency criterion for price impact functions in limit order markets is proposed that prohibits chain arbitrage exploitation. Both the bid-ask spread and the feedback of sequential market orders of the same kind onto both sides of the order book are essential to ensure consistency at the smallest time scale. All the stocks investigated in Paris Stock Exchange have consistent price impact functions.