Showing papers by "Anirban Chakraborti published in 2019"

Complex Market Dynamics in the Light of Random Matrix Theory

Abstract: We present a brief overview of random matrix theory (RMT) with the objectives of highlighting the computational results and applications in financial markets as complex systems An oft-encountered problem in computational finance is the choice of an appropriate epoch over which the empirical cross-correlation return matrix is computed A long epoch would smoothen the fluctuations in the return time series and suffers from non-stationarity, whereas a short epoch results in noisy fluctuations in the return time series and the correlation matrices turn out to be highly singular An effective method to tackle this issue is the use of the power mapping, where a non-linear distortion is applied to a short epoch correlation matrix The value of distortion parameter controls the noise-suppression The distortion also removes the degeneracy of zero eigenvalues Depending on the correlation structures, interesting properties of the eigenvalue spectra are found We simulate different correlated Wishart matrices to compare the results with empirical return matrices computed using the SP (ii) Characterization of catastrophic instabilities (market crashes)

Multi-layered network structure: Relationship between financial and macroeconomic dynamics

Abstract: We demonstrate using multi-layered networks, the existence of an empirical linkage between the dynamics of the financial network constructed from the market indices and the macroeconomic networks constructed from macroeconomic variables such as trade, foreign direct investments, etc. for several countries across the globe. The temporal scales of the dynamics of the financial variables and the macroeconomic fundamentals are very different, which make the empirical linkage even more interesting and significant. Also, we find that there exist in the respective networks, core-periphery structures (determined through centrality measures) that are composed of similar set of countries—a result that may be related through the ‘gravity model’ of the country-level macroeconomic networks. Thus, from a multi-lateral openness perspective, we elucidate that for individual countries, larger trade connectivity is positively associated with higher financial return correlations. Furthermore, we show that the Economic Complexity Index and the equity markets have a positive relationship among themselves, as is the case for Gross Domestic Product. The data science methodology using network theory, coupled with standard econometric techniques constitute a new approach to studying multi-level economic phenomena in a comprehensive manner.

Hamiltonian energy as an efficient approach to identify the significant key regulators in biological networks.

Abstract: The topological characteristics of biological networks enable us to identify the key nodes in terms of modularity. However, due to a large size of the biological networks with many hubs and functional modules across intertwined layers within the network, it often becomes difficult to accomplish the task of identifying potential key regulators. We use for the first time a generalized formalism of Hamiltonian Energy (HE) with a recursive approach. The concept, when applied to the Apoptosis Regulatory Gene Network (ARGN), helped us identify 11 Motif hubs (MHs), which influenced the network up to motif levels. The approach adopted allowed to classify MHs into 5 significant motif hubs (S-MHs) and 6 non-significant motif hubs (NS-MHs). The significant motif hubs had a higher HE value and were considered as high-active key regulators; while the non-significant motif hubs had a relatively lower HE value and were considered as low-active key regulators, in network control mechanism. Further, we compared the results of the HE analyses with the topological characterization, after subjecting to the three conditions independently: (i) removing all MHs, (ii) removing only S-MHs, and (iii) removing only NS-MHs from the ARGN. This procedure allowed us to cross-validate the role of 5 S-MHs, NFk-B1, BRCA1, CEBPB, AR, and POU2F1 as the potential key regulators. The changes in HE calculations further showed that the removal of 5 S-MHs could cause perturbation at all levels of the network, a feature not discernible by topological analysis alone.

Phase separation and scaling in correlation structures of financial markets

Abstract: Financial markets, being spectacular examples of complex systems, display rich correlation structures among price returns of different assets. The correlation structures change drastically, akin to phase transitions in physical phenomena, as do the influential stocks (leaders) and sectors (communities), during market events like crashes. It is crucial to detect their signatures for timely intervention or prevention. Here we use eigenvalue decomposition and eigen-entropy, computed from eigen-centralities of different stocks in the cross-correlation matrix, to extract information about the disorder in the market. We construct a `phase space', where different market events (bubbles, crashes, etc.) undergo phase separation and display order-disorder transitions. An entropy functional exhibits scaling behavior. We propose a generic indicator that facilitates the continuous monitoring of the internal structure of the market -- important for managing risk and stress-testing the financial system. Our methodology would help in understanding and foreseeing tipping points or fluctuation patterns in complex systems.

Eigen-entropy measure to study phase separation in market behavior

Abstract: One of the spectacular examples of a complex system is the financial market, which displays rich correlation structures among price returns of different assets. The eigenvalue decomposition of a correlation matrix into partial correlations - market, group and random modes, enables identification of dominant stocks or "influential leaders" and sectors or "communities". The correlation-based network of leaders and communities changes with time, especially during market events like crashes, bubbles, etc. Using a novel entropy measure - eigen-entropy, computed from the eigen-centralities (ranks) of different stocks in the correlation-network, we extract information about the "disorder" (or randomness) in the market and its modes. The relative-entropy measures computed for these modes enable us to construct a "phase space", where the different market events undergo "phase-separation" and display "order-disorder" transitions, as observed in critical phenomena in physics. We choose the US S&P-500 and Japanese Nikkei-225 financial markets, over a 32-year period, and study the evolution of the cross-correlation matrices computed over different short time-intervals or "epochs", and their corresponding eigen-entropies. We compare and contrast the empirical results against the numerical results for Wishart orthogonal ensemble (WOE), which has the maximum disorder (randomness) and hence, the highest eigen-entropy. This new methodology helps us to better understand market dynamics, and characterize the events in different phases as anomalies, bubbles, crashes, etc. This can be easily adapted and broadly applied to the studies of other complex systems such as in brain science or environment.

Tailoring optical and magnetic properties of molybdenum disulphide nanosheets by incorporating plasmonic gold nanoparticles

Abstract: The present paper deals with the systematic growth of plasmonic gold nanoparticles (Au NPs) on molybdenum disulphide (MoS$_2$) nanosheets as well as the effect of Au NPs on the optical and magnetic properties. The crystalline nature of the nanocomposites is confirmed by X-ray diffraction and transmission electron microscopic techniques. The optical properties are characterized using absorption and Raman spectroscopic techniques. The electron paramagnetic resonance technique is used to study the magnetic response of the nanocomposites. The paper attempts to gain a fundamental understanding of the two-dimensional nanomaterial-based composites for their applications in the magnetic and optical devices.

Distinguishing Two Different Mental States of Human Thought Using Soft Computing Approaches

Abstract: Electroencephalograph (EEG) is useful modality nowadays which is utilized to capture cognitive activities in the form of a signal representing the potential for a given period. Brain–Computer Interface (BCI) systems are one of the practical application of EEG signal. Response to mental task is a well-known type of BCI systems which augments the life of disabled persons to communicate their core needs to machines that can able to distinguish among mental states corresponding to thought responses to the EEG. The success of classification of these mental tasks depends on the pertinent set formation of features (analysis, extraction, and selection) of the EEG signals for the classification process. In the recent past, a filter-based heuristic technique, Empirical Mode Decomposition (EMD), is employed to analyze EEG signal. EMD is a mathematical technique which is suitable to analyze a nonstationary and nonlinear signal such as EEG. In this work, three-stage feature set formation from EEG signal for building classification model is suggested to distinguish different mental states. In the first stage, the signal is broken into a number of oscillatory functions through EMD algorithm. The second stage involves compact representation in terms of eight different statistics (features) obtained from each oscillatory function. It has also observed that not all features are relevant, therefore, there is need to select most relevant features from the pool of the formed features which is carried out in the third stage. Four well-known univariate feature selection algorithms are investigated in combination with EMD algorithm for forming the feature vectors for further classification. Classification is carried out with help of learning the support vector machine (SVM) classification model. Experimental result on a publicly available dataset shows the superior performance of the proposed approach.

Eigen-entropy measure to study phase separation in market behavior

Abstract: Financial markets, being spectacular examples of complex systems, display rich correlation structures among price returns of different assets. The correlation structures change drastically, akin to phase transitions in physical phenomena, as do the influential stocks (leaders) and sectors (communities), during market events like crashes. It is crucial to detect their signatures for timely intervention or prevention. Here we use eigenvalue decomposition and eigen-entropy, computed from eigen-centralities of different stocks in the cross-correlation matrix, to extract information about the disorder in the market. We construct a `phase space', where different market events (bubbles, crashes, etc.) undergo phase separation and display order-disorder transitions. An entropy functional exhibits scaling behavior. We propose a generic indicator that facilitates the continuous monitoring of the internal structure of the market -- important for managing risk and stress-testing the financial system. Our methodology would help in understanding and foreseeing tipping points or fluctuation patterns in complex systems.