On the efficiency of sovereign bond markets

The existence of memory in financial time series has been extensively studied for several stock markets around the world by means of different approaches. However, fixed income markets, i.e. those where corporate and sovereign bonds are traded, have been much less studied. We believe that, given the relevance of these markets, not only from the investors’, but also from the issuers’ point of view (government and firms), it is necessary to fill this gap in the literature. In this paper, we study the sovereign market efficiency of thirty bond indices of both developed and emerging countries, using an innovative statistical tool in the financial literature: the complexity-entropy causality plane. This representation space allows us to establish an efficiency ranking of different markets and distinguish different bond market dynamics. We conclude that the classification derived from the complexity-entropy causality plane is consistent with the qualifications assigned by major rating companies to the sovereign instruments. Additionally, we find a correlation between permutation entropy, economic development and market size that could be of interest for policy makers and investors.     

Complexity-entropy causality plane: A useful approach to quantify the stock market inefficiency

The complexity-entropy causality plane has been recently introduced as a powerful tool for discriminating Gaussian from non-Gaussian process and different degrees of correlations [O.A. Rosso, H.A. Larrondo, M.T. Martín, A. Plastino, M.A. Fuentes, Distinguishing noise from chaos, Phys. Rev. Lett. 99 (2007) 154102]. We propose to use this representation space to distinguish the stage of stock market development. Our empirical results demonstrate that this statistical physics approach is useful, allowing a more refined classification of stock market dynamics.     

Complexity-entropy causality plane: A useful approach for distinguishing songs

Nowadays we are often faced with huge databases resulting from the rapid growth of data storage technologies. This is particularly true when dealing with music databases. In this context, it is essential to have techniques and tools able to discriminate properties from these massive sets. In this work, we report on a statistical analysis of more than ten thousand songs aiming to obtain a complexity hierarchy. Our approach is based on the estimation of the permutation entropy combined with an intensive complexity measure, building up the complexity-entropy causality plane. The results obtained indicate that this representation space is very promising to discriminate songs as well as to allow a relative quantitative comparison among songs. Additionally, we believe that the here-reported method may be applied in practical situations since it is simple, robust and has a fast numerical implementation.     

Dynamic behavior of temperature field in a buoyancy-driven turbulent fire

We study the dynamic behavior of temperature field in a buoyancy-driven turbulent fire from the viewpoints of symbolic dynamics, complex networks, and statistical complexity. The permutation entropy and the horizontal visibility network entropy allow us to capture the subtle changes in temperature fluctuations. The possible existence of deterministic chaos in temperature fluctuations, as well as in streamwise flow velocity fluctuations [Takagi et al., Phys. Rev. E 96 (2017) 052223], is clearly verified using the multiscale complexity-entropy causality plane.     

Revisiting the European sovereign bonds with a permutation-information-theory approach

In this paper we study the evolution of the informational efficiency in its weak form for seventeen European sovereign bonds time series. We aim to assess the impact of two specific economic situations in the hypothetical random behavior of these time series: the establishment of a common currency and a wide and deep financial crisis. In order to evaluate the informational efficiency we use permutation quantifiers derived from information theory. Specifically, time series are ranked according to two metrics that measure the intrinsic structure of their correlations: permutation entropy and permutation statistical complexity. These measures provide the rectangular coordinates of the complexity-entropy causality plane; the planar location of the time series in this representation space reveals the degree of informational efficiency. According to our results, the currency union contributed to homogenize the stochastic characteristics of the time series and produced synchronization in the random behavior of them. Additionally, the 2008 financial crisis uncovered differences within the apparently homogeneous European sovereign markets and revealed country-specific characteristics that were partially hidden during the monetary union heyday.     

Distinguishing noise from chaos

Chaotic systems share with stochastic processes several properties that make them almost undistinguishable. In this communication we introduce a representation space, to be called the complexity-entropy causality plane. Its horizontal and vertical axis are suitable functionals of the pertinent probability distribution, namely, the entropy of the system and an appropriate statistical complexity measure, respectively. These two functionals are evaluated using the Bandt-Pompe recipe to assign a probability distribution function to the time series generated by the system. Several well-known model-generated time series, usually regarded as being of either stochastic or chaotic nature, are analyzed so as to illustrate the approach. The main achievement of this communication is the possibility of clearly distinguishing between them in our representation space, something that is rather difficult otherwise.     

Parametric and nonparametric Granger causality testing: Linkages between international stock markets

This study investigates long-term linear and nonlinear causal linkages among eleven stock markets, six industrialized markets and five emerging markets of South-East Asia. We cover the period 1987-2006, taking into account the on-set of the Asian financial crisis of 1997. We first apply a test for the presence of general nonlinearity in vector time series. Substantial differences exist between the pre- and post-crisis period in terms of the total number of significant nonlinear relationships. We then examine both periods, using a new nonparametric test for Granger noncausality and the conventional parametric Granger noncausality test. One major finding is that the Asian stock markets have become more internationally integrated after the Asian financial crisis. An exception is the Sri Lankan market with almost no significant long-term linear and nonlinear causal linkages with other markets. To ensure that any causality is strictly nonlinear in nature, we also examine the nonlinear causal relationships of VAR filtered residuals and VAR filtered squared residuals for the post-crisis sample. We find quite a few remaining significant bi- and uni-directional causal nonlinear relationships in these series. Finally, after filtering the VAR-residuals with GARCH-BEKK models, we show that the nonparametric test statistics are substantially smaller in both magnitude and statistical significance than those before filtering. This indicates that nonlinear causality can, to a large extent, be explained by simple volatility effects.     

Forbidden patterns, permutation entropy and stock market inefficiency

In this paper we introduce two new quantifiers for the stock market inefficiency: the number of forbidden patterns and the normalized permutation entropy. They are model-independent measures, thus they have more general applicability. We find robust evidence that degree of market inefficiency is positively correlated with the number of forbidden patterns and negatively correlated with the permutation entropy. Our empirical results suggest that these two physical tools are useful to discriminate the stage of stock market development and can be easily implemented.     

The correlation length of commodity markets 1. Empirical evidence

It is a common belief nowadays that the world economy is fairly well “integrated”. Yet, this belief often turns out to be in contradiction with empirical evidence. As a matter of fact the way distant markets interact is a question that has largely been ignored by economists. In this series of two papers we examine the role that space, that is to say geographical distance, plays in the economics of commodity markets. The first of these papers presents the empirical evidence while the second develops a theoretical framework. The empirical enquiry discloses several noteworthy features, e.g. (i) with respect to spatial interaction there is a sharp contrast between stock markets and commodity markets. While there is almost perfect spatial arbitrage in the first case, this is not true for commodity markets. (ii) In spite of their chaotic behavior in the course of time commodity prices display well defined spatial patterns, (iii) as in statistical physics and fluid dynamics interactions can be described in terms of correlation length. The correlation length of a set of markets is seen to increase along with the number of transactions; it also increases when transport costs decline as was the case during the “transportation revolution” of the mid-nineteenth century. Using the notion of correlation length one is able to give a quantitative meaning to the otherwise ill-defined concept of market integration. Received 17 May 1999 and Received in final form 31 May 1999     

Dependence structure of the commodity and stock markets,and relevant multi-spread strategy

Understanding the dependence structure between the commodity and stock markets is a crucial issue in constructing a portfolio. It can also help us to discover new opportunities to implement spread trading using multiple assets classified in the two different markets. This study analyzed the dependence structure of the commodity and stock markets using the random matrix theory technique and network analysis. Our results show that the stock and commodity markets must be handled as completely separated asset classes except for the oil and gold markets, so the performance enhancement of the mean-variance portfolio is significant as expected. In light of the fact that WTI 1 month futures and four oil-related stocks are strongly correlated, they were selected as basic ingredients to complement the multi-spread convergence trading strategy using a machine learning technique called the AdaBoost algorithm. The performance of this strategy for non-myopic investors, who can endure short-term loss, can be enhanced significantly on a risk measurement basis.     

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.     

Permutation complexity via duality between values and orderings

We study the permutation complexity of finite-state stationary stochastic processes based on a duality between values and orderings between values. First, we establish a duality between the set of all words of a fixed length and the set of all permutations of the same length. Second, on this basis, we give an elementary alternative proof of the equality between the permutation entropy rate and the entropy rate for a finite-state stationary stochastic processes first proved in [J.M. Amigó, M.B. Kennel, L. Kocarev, The permutation entropy rate equals the metric entropy rate for ergodic information sources and ergodic dynamical systems, Physica D 210 (2005) 77-95]. Third, we show that further information on the relationship between the structure of values and the structure of orderings for finite-state stationary stochastic processes beyond the entropy rate can be obtained from the established duality. In particular, we prove that the permutation excess entropy is equal to the excess entropy, which is a measure of global correlation present in a stationary stochastic process, for finite-state stationary ergodic Markov processes.     

Investigating the change of causality in emerging property markets during the financial tsunami

In this paper, we employ the multivariate CUSUM (cumulative sum) test for covariance structure as well as the renormalized partial directed coherence (PDC) method to capture the structural causality change of real estate stock indices of five emerging Asian countries and regions (i.e., Thailand, Malaysia, South Korea, PR China, and Taiwan). Meanwhile, we develop a method to make the comparison of renormalized PDC more intuitive and a set of criteria to measure the result. One of our findings indicates that the regional influence of the Chinese real estate stock market on the causality structure of the five markets has arisen under the effect of the financial tsunami.     

A network analysis of the Chinese stock market

In many practical important cases, a massive dataset can be represented as a very large network with certain attributes associated with its vertices and edges. Stock markets generate huge amounts of data, which can be use for constructing the network reflecting the market’s behavior. In this paper, we use a threshold method to construct China’s stock correlation network and then study the network’s structural properties and topological stability. We conduct a statistical analysis of this network and show that it follows a power-law model. We also detect components, cliques and independent sets in this network. These analyses allows one to apply a new data mining technique of classifying financial instruments based on stock price data, which provides a deeper insight into the internal structure of the stock market. Moreover, we test the topological stability of this network and find that it displays a topological robustness against random vertex failures, but it is also fragile to intentional attacks. Such a network stability property would be also useful for portfolio investment and risk management.     

Comparing the structure of an emerging market with a mature one under global perturbation

In this paper we investigate the Tehran stock exchange (TSE) and Dow Jones Industrial Average (DJIA) in terms of perturbed correlation matrices. To perturb a stock market, there are two methods, namely local and global perturbation. In the local method, we replace a correlation coefficient of the cross-correlation matrix with one calculated from two Gaussian-distributed time series, whereas in the global method, we reconstruct the correlation matrix after replacing the original return series with Gaussian-distributed time series. The local perturbation is just a technical study. We analyze these markets through two statistical approaches, random matrix theory (RMT) and the correlation coefficient distribution. By using RMT, we find that the largest eigenvalue is an influence that is common to all stocks and this eigenvalue has a peak during financial shocks. We find there are a few correlated stocks that make the essential robustness of the stock market but we see that by replacing these return time series with Gaussian-distributed time series, the mean values of correlation coefficients, the largest eigenvalues of the stock markets and the fraction of eigenvalues that deviate from the RMT prediction fall sharply in both markets. By comparing these two markets, we can see that the DJIA is more sensitive to global perturbations. These findings are crucial for risk management and portfolio selection.     

Alternation of different fluctuation regimes in the stock market dynamics

Based on the tick-by-tick stock prices from the German and American stock markets, we study the statistical properties of the distribution of the individual stocks and the index returns in highly collective and noisy intervals of trading, separately. We show that periods characterized by the strong inter-stock couplings can be associated with the distributions of index fluctuations which reveal more pronounced tails than in the case of weaker couplings in the market. During periods of strong correlations in the German market these distributions can even reveal an apparent Lévy-stable component.     

The structure and resilience of financial market networks

Financial markets can be viewed as a highly complex evolving system that is very sensitive to economic instabilities. The complex organization of the market can be represented in a suitable fashion in terms of complex networks, which can be constructed from stock prices such that each pair of stocks is connected by a weighted edge that encodes the distance between them. In this work, we propose an approach to analyze the topological and dynamic evolution of financial networks based on the stock correlation matrices. An entropy-related measurement is adopted to quantify the robustness of the evolving financial market organization. It is verified that the network topological organization suffers strong variation during financial instabilities and the networks in such periods become less robust. A statistical robust regression model is proposed to quantity the relationship between the network structure and resilience. The obtained coefficients of such model indicate that the average shortest path length is the measurement most related to network resilience coefficient. This result indicates that a collective behavior is observed between stocks during financial crisis. More specifically, stocks tend to synchronize their price evolution, leading to a high correlation between pair of stock prices, which contributes to the increase in distance between them and, consequently, decrease the network resilience.     

Stylized facts in internal rates of return on stock index and its derivative transactions

Universal features in stock markets and their derivative markets are studied by means of probability distributions in internal rates of return on buy and sell transaction pairs. Unlike the stylized facts in normalized log returns, the probability distributions for such single asset encounters incorporate the time factor by means of the internal rate of return, defined as the continuous compound interest. Resulting stylized facts are shown in the probability distributions derived from the daily series of TOPIX, S & P 500 and FTSE 100 index close values. The application of the above analysis to minute-tick data of NIKKEI 225 and its futures market, respectively, reveals an interesting difference in the behavior of the two probability distributions, in case a threshold on the minimal duration of the long position is imposed. It is therefore suggested that the probability distributions of the internal rates of return could be used for causality mining between the underlying and derivative stock markets. The highly specific discrete spectrum, which results from noise trader strategies as opposed to the smooth distributions observed for fundamentalist strategies in single encounter transactions may be useful in deducing the type of investment strategy from trading revenues of small portfolio investors.     

Statistical mechanics and financial markets: Antagony between derivatives and market self-regulation

We establish specific correspondences between notions of economics and statistical mechanics. There are several situations wherein a rather accurate correspondence has already been established, for instance in utility theory for exchange economy with quasilinear utility function, which has been mapped to analogous thermodynamics. We discuss how statistical mechanics can be applied to define the efficiency of financial markets, via a mapping of stock fluctuations to the Random Energy Model (REM) at particular temperatures. We introduce the concept of reflection in economics; the effective reflection number, in particular, is found to be crucial in understanding the self-regulation of the market. We also establish a qualitative similarity between market with derivatives and certain statistical mechanics models. Such an analogy supports a hypothesis that financial derivatives are antagonistic to the self-regulation of financial markets. As a whole, our analysis is complementary to established concepts and methods of neoclassical economics for markets without derivatives.     

An Entropy-Based Approach to Measurement of Stock Market Depth

The aim of this study is to investigate market depth as a stock market liquidity dimension. A new methodology for market depth measurement exactly based on Shannon information entropy for high-frequency data is introduced and utilized. The proposed entropy-based market depth indicator is supported by an algorithm inferring the initiator of a trade. This new indicator seems to be a promising liquidity measure. Both market entropy and market liquidity can be directly measured by the new indicator. The findings of empirical experiments for real-data with a time stamp rounded to the nearest second from the Warsaw Stock Exchange (WSE) confirm that the new proxy enables us to effectively compare market depth and liquidity for different equities. Robustness tests and statistical analyses are conducted. Furthermore, an intra-day seasonality assessment is provided. Results indicate that the entropy-based approach can be considered as an auspicious market depth and liquidity proxy with an intuitive base for both theoretical and empirical analyses in financial markets.