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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…
Causal inference seeks to identify cause-and-effect interactions in coupled systems. A recently proposed method by Liang detects causal relations by quantifying the direction and magnitude of information flow between time series. The…
Conformal prediction offers a practical framework for distribution-free uncertainty quantification, providing finite-sample coverage guarantees under relatively mild assumptions on data exchangeability. However, these assumptions cease to…
We study theoretical and empirical aspects of the mean exit time of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a…
We propose a stochastic process for stock movements that, with just one source of Brownian noise, has an instantaneous volatility that rises from a type of statistical feedback across many time scales. This results in a stationary…
We show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of price fluctuations. The central result of the…
We consider the long time asymptotic behavior of a large system of $N$ linear differential equations with random coefficients. We allow for general elliptic correlation structures among the coefficients, thus we substantially generalize our…
We propose a reduced form set of two coupled continuous time equations linking the price of a representative asset and the price of a bond, the later quantifying the cost of borrowing. The feedbacks between asset prices and bonds are…
Recently the interest of researchers has shifted from the analysis of synchronous relationships of financial instruments to the analysis of more meaningful asynchronous relationships. Both of those analyses are concentrated only on…
The time-dependent exchange-correlation potential has an unusual task in directing fictitious non-interacting electrons to move with exactly the same probability density as true interacting electrons. This has intriguing implications for…
When an item goes out of stock, sales transaction data no longer reflect the original customer demand, since some customers leave with no purchase while others substitute alternative products for the one that was out of stock. Here we…
We investigated distributions of short term price trends for high frequency stock market data. A number of trends as a function of their lengths was measured. We found that such a distribution does not fit to results following from an…
For a class of idealized chaotic systems (hyperbolic systems) correlations decay exponentially in time. This result is asymptotic and rigorous. The decay rate is related to the Ruelle-Pollicott resonances. Nearly all chaotic model systems,…
Stochastic processes with renewal properties are powerful tools for modeling systems where memory effects and long-time correlations play a significant role. In this work, we study a broad class of renewal processes where a variable's value…
Fluctuations in parameters that are typically treated as fixed play a crucial role in the behavior of complex systems. However, to date, we lack a general non-equilibrium thermodynamic treatment of such a complex system. In this Letter, to…
The two-dimensional random-bond Ising model is numerically studied on long strips by transfer-matrix methods. It is shown that the rate of decay of correlations at criticality, as derived from averages of the two largest Lyapunov exponents…
One of the fundamental steps toward understanding a complex system is identifying variation at the scale of the system's components that is most relevant to behavior on a macroscopic scale. Mutual information provides a natural means of…
Couplings in complex real-world systems are often nonlinear and scale-dependent. In many cases, it is crucial to consider a multitude of interlinked variables and the strengths of their correlations to adequately fathom the dynamics of a…
Information diagram and the I-measure are useful mnemonics where random variables are treated as sets, and entropy and mutual information are treated as a signed measure. Although the I-measure has been successful in machine proofs of…
Recovering properties of correlation functions is typically challenging. On one hand, experimentally, it requires measurements with a temporal resolution finer than the system's dynamics. On the other hand, analytical or numerical analysis…