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 stability criterion for financial markets

Using the theory of random cluster models, we give a stability criterion for financial markets with random communications between agents. Received 25 September 1999 and Received in final form 2 October 1999     

Untangling complex networks: Risk minimization in financial markets through accessible spin glass ground states

Recurrent international financial crises inflict significant damage to societies and stress the need for mechanisms or strategies to control risk and tamper market uncertainties. Unfortunately, the complex network of market interactions often confounds rational approaches to optimize financial risks. Here we show that investors can overcome this complexity and globally minimize risk in portfolio models for any given expected return, provided the margin requirement remains below a critical, empirically measurable value. In practice, for markets with centrally regulated margin requirements, a rational stabilization strategy would be keeping margins small enough. This result follows from ground states of the random field spin glass Ising model that can be calculated exactly through convex optimization when relative spin coupling is limited by the norm of the network’s Laplacian matrix. In that regime, this novel approach is robust to noise in empirical data and may be also broadly relevant to complex networks with frustrated interactions that are studied throughout scientific fields.     

A Bayesian Networks approach to Operational Risk

A system for Operational Risk management based on the computational paradigm of Bayesian Networks is presented. The algorithm allows the construction of a Bayesian Network targeted for each bank and takes into account in a simple and realistic way the correlations among different processes of the bank. The internal losses are averaged over a variable time horizon, so that the correlations at different times are removed, while the correlations at the same time are kept: the averaged losses are thus suitable to perform the learning of the network topology and parameters; since the main aim is to understand the role of the correlations among the losses, the assessments of domain experts are not used. The algorithm has been validated on synthetic time series. It should be stressed that the proposed algorithm has been thought for the practical implementation in a mid or small sized bank, since it has a small impact on the organizational structure of a bank and requires an investment in human resources which is limited to the computational area.     

Modified DFA and DCCA approach for quantifying the multiscale correlation structure of financial markets

We use multiscale detrended fluctuation analysis (MSDFA) and multiscale detrended cross-correlation analysis (MSDCCA) to investigate auto-correlation (AC) and cross-correlation (CC) in the US and Chinese stock markets during 1997–2012. The results show that US and Chinese stock indices differ in terms of their multiscale AC structures. Stock indices in the same region also differ with regard to their multiscale AC structures. We analyze AC and CC behaviors among indices for the same region to determine similarity among six stock indices and divide them into four groups accordingly. We choose S&P500, NQCI, HSI, and the Shanghai Composite Index as representative samples for simplicity. MSDFA and MSDCCA results and average MSDFA spectra for local scaling exponents (LSEs) for individual series are presented. We find that the MSDCCA spectrum for LSE CC between two time series generally tends to be greater than the average MSDFA LSE spectrum for individual series. We obtain detailed multiscale structures and relations for CC between the four representatives. MSDFA and MSDCCA with secant rolling windows of different sizes are then applied to reanalyze the AC and CC. Vertical and horizontal comparisons of different window sizes are made. The MSDFA and MSDCCA results for the original window size are confirmed and some new interesting characteristics and conclusions regarding multiscale correlation structures are obtained.     

A new approach to assessing the performance of noise indices in buildings

The results of a wide acoustic environment survey are presented. Sound pressure measurements were carried out in a group of offices. These measurements lasted for five minutes and the resulting noise spectra were used to calculate the most significant acoustic parameters. During each measurement a questionnaire was administered to workers near each measuring position. The questionnaire asked them to indicate their subjective judgement about noise annoyance, noise loudness and dissatisfaction induced by noise present in the environment. The aim of the research was to investigate the performance of the measured noise indices in describing subjective responses to noise. A new method to calculate the average subjective responses is proposed. The performance of the noise indices was studied by means of linear regression analysis. Finally the A-weighted equivalent sound pressure level proved to be the best index among those analysed in describing subjective auditory sensations.     

A DFA approach for assessing asymmetric correlations

Here we propose a method, based on detrended fluctuation analysis, to investigate asymmetric correlations in nonstationary time series. The aim is to show that, for a certain range of time scales, different scaling properties are found if signal trending is either positive and negative. We illustrate the method by selected examples from physics and finance.     

An econophysics approach to analyse uncertainty in financial markets: an application to the Portuguese stock market

In recent years there has been a closer interrelationship between several scientific areas trying to obtain a more realistic and rich explanation of the natural and social phenomena. Among these it should be emphasized the increasing interrelationship between physics and financial theory. In this field the analysis of uncertainty, which is crucial in financial analysis, can be made using measures of physics statistics and information theory, namely the Shannon entropy. One advantage of this approach is that the entropy is a more general measure than the variance, since it accounts for higher order moments of a probability distribution function. An empirical application was made using data collected from the Portuguese Stock Market.     

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     

A long-range memory stochastic model of the return in financial markets

We present a nonlinear stochastic differential equation (SDE) which mimics the probability density function (PDF) of the return and the power spectrum of the absolute return in financial markets. Absolute return as a measure of market volatility is considered in the proposed model as a long-range memory stochastic variable. The SDE is obtained from the analogy with an earlier proposed model of trading activity in the financial markets and generalized within the nonextensive statistical mechanics framework. The proposed stochastic model generates time series of the return with two power law statistics, i.e., the PDF and the power spectral density, reproducing the empirical data for the one-minute trading return in the NYSE.     

A mini-review on econophysics:Comparative study of Chinese and western financial markets

We present a review of our recent research in econophysics, and focus on the comparative study of Chinese and western financial markets. By virtue of concepts and methods in statistical physics, we investigate the time correlations and spatial structure of financial markets based on empirical high-frequency data. We discover that the Chinese stock market shares common basic properties with the western stock markets, such as the fat-tail probability distribution of price returns, the long-range auto-correlation of volatilities, and the persistence probability of volatilities, while it exhibits very different higher-order time correlations of price returns and volatilities, spatial correlations of individual stock prices, and large-fluctuation dynamic behaviors. Furthermore, multi-agent-based models are developed to simulate the microscopic interaction and dynamic evolution of the stock markets.     

Dynamics of real financial markets: A reply to Frank’s comment

This reply addresses the assertion in the comment of T.D. Frank [T.D. Frank, Physica A 387 (2008) 773] on our paper [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343] that the approach to modeling financial markets that we propose is unrealistic. In our paper, we considered variable diffusion processes that have a diffusion coefficient that varies with both position (return in finance) and time, and used them to show that measuring a Hurst exponent H≠1/2 in a time series does not necessarily imply correlations between increments. We also proposed that such a variable diffusion process is the underlying stochastic process governing the dynamics of financial markets. Frank asserts that this is unrealistic because variable diffusion processes with H≠1/2 are driven with a “force” that varies in time as a power law. He claims, instead, that markets obey nonextensive thermostatistics. We discuss evidence from a recently published empirical study of the Euro-Dollar exchange rate [K.E. Bassler, J.L. McCauley, G.H. Gunaratne, PNAS 104 (2007) 17287] that shows that the market can be described with a variable diffusion process, but is inconsistent with nonextensive thermostatistics. This evidence demonstrates that our modeling approach is realistic and accurate.     

A model for the evaluation of systemic risk in stock markets

Systemic risk refers to the possibility of a collapse of an entire financial system or market, differing from the risk associated with any particular individual or a group pertaining to the system, which may include banks, government, brokers, and creditors. After the 2008 financial crisis, a significant amount of effort has been directed to the study of systemic risk and its consequences around the world. Although it is very difficult to predict when people begin to lose confidence in a financial system, it is possible to model the relationships among the stock markets of different countries and perform a Monte Carlo-type analysis to study the contagion effect. Because some larger and stronger markets influence smaller ones, a model inspired by a catalytic chemical model is proposed. In chemical reactions, reagents with higher concentrations tend to favor their conversion to products. In order to modulate the conversion process, catalyzers may be used. In this work, a mathematical modeling is proposed with bases on the catalytic chemical reaction model. More specifically, the Hang Seng and Dow Jones indices are assumed to dominate Ibovespa (the Brazilian Stock Market index), such that the indices of strong markets are taken as being analogous to the concentrations of the reagents and the indices of smaller markets as concentrations of products. The role of the catalyst is to model the degree of influence of one index on another. The actual data used to fit the model parameter consisted of the Hang Seng index, Dow Jones index, and Ibovespa, since 1993. “What if” analyses were carried out considering some intervention policies.     

Information flow between stock markets: A Koopman decomposition approach

Stock markets in the world are linked by complicated and dynamical relationships into a temporal network.Extensive works have provided us with rich findings from the topological properties and their evolutionary trajectories,but the underlying dynamical mechanism is still not in order.In the present work,we proposed a technical scheme to reveal the dynamical law from the temporal network.The index records for the global stock markets form a multivariate time series.One separates the series into segments and calculates the information flows between the markets,resulting in a temporal market network representing the state and its evolution.Then the technique of the Koopman decomposition operator is adopted to find the law stored in the information flows.The results show that the stock market system has a high flexibility,i.e.,it jumps easily between different states.The information flows mainly from high to low volatility stock markets.And the dynamical process of information flow is composed of many dynamic modes distribute homogenously in a wide range of periods from one month to several ten years,but there exist only nine modes dominating the macroscopic patterns.     

Linkages between international stock markets: A multivariate long-memory approach

This paper aims to analyze the linkages between international stock markets and to search for an optimum model for analyzing their interactions taking into consideration their geographical location, using the vector fractionally integrated autoregressive moving-average (VARFIMA) model. This model has not so far been employed in examining the interdependence among the stock markets of Germany, Japan, the UK, and the USA. The results of the paper show that there is an interconnection among the stock markets of these countries.