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Information theoretic measures (entropies, entropy rates, mutual information) are nowadays commonly used in statistical signal processing for real-world data analysis. The present work proposes the use of Auto Mutual Information (Mutual…
Theoretical computer science plays an important role in the understanding of social networks and their properties. We can model information rippling throughout social networks, or the opinions of social media users for example, using graph…
People are often divided into conformists and contrarians, the former tending to align to the majority opinion in their neighborhood and the latter tending to disagree with that majority. In practice, however, the contrarian tendency is…
We study the activity, i.e., the number of transactions per unit time, of financial markets. Using the diffusion entropy technique we show that the autocorrelation of the activity is caused by the presence of peaks whose time distances are…
Using empirical data from a social media site (Twitter) and on trading volumes of financial securities, we analyze the correlated human activity in massive social organizations. The activity, typically excited by real-world events and…
We consider dynamical systems evolving near an equilibrium statistical state where the interest is in modelling long term behavior that is consistent with thermodynamic constraints. We adjust the distribution using an entropy-optimizing…
The economical world consists of a highly interconnected and interdependent network of firms. Here we develop temporal and structural network tools to analyze the state of the economy. Our analysis indicates that a strong clustering can be…
We propose a general interpretation for long-range correlation effects in the activity and volatility of financial markets. This interpretation is based on the fact that the choice between `active' and `inactive' strategies is subordinated…
We use a new method of studying the Hurst exponent with time and scale dependency. This new approach allow us to recover the major events affecting worldwide markets (such as the September 11th terrorist attack) and analyze the way those…
We give a new predictive mathematical model for macroeconomics, which deals specifically with asset prices and earnings fluctuations, in the presence of a dynamic economy involving mergers, acquisitions, and hostile takeovers. Consider a…
This paper proposes a simple and parsimonious discrete-time simulation model to describe the endogenous formation and periodic collapse of financial bubbles. While existing literature has extensively explored the statistical properties of…
Statistical arbitrage strategies, such as pairs trading and its generalizations, rely on the construction of mean-reverting spreads enjoying a certain degree of predictability. Gaussian linear state-space processes have recently been…
Financial markets are nonlinear with complexity, where different types of assets are traded between buyers and sellers, each having a view to maximize their Return on Investment (ROI). Forecasting market trends is a challenging task since…
This research presents a novel approach to predicting option movements by analyzing residual transactions, which are trades that deviate from standard hedging activities. Unlike traditional methods that primarily focus on open interest and…
This paper explores neural network-based approaches for algorithmic trading in cryptocurrency markets. Our approach combines multi-timeframe trend analysis with high-frequency direction prediction networks, achieving positive risk-adjusted…
We investigate the large-volatility dynamics in financial markets, based on the minute-to-minute and daily data of the Chinese Indices and German DAX. The dynamic relaxation both before and after large volatilities is characterized by a…
We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure.…
A new class of stochastic processes called independent and periodically identically distributed (i.p.i.d.) processes is defined to capture periodically varying statistical behavior. Algorithms are proposed to detect changes in such i.p.i.d.…
We introduce and study a non-equilibrium continuous-time dynamical model of the price of a single asset traded by a population of heterogeneous interacting agents in the presence of uncertainty and regulatory constraints. The model takes…
We introduce new kinetic equations modeling opinion dynamics inside a population of individuals, whose propensity to interact with each other is described by their level of social activity. We show that opinion polarization can arise among…