Related papers: Detecting discrete processes with the Epps effect
We study the relationship between dynamical properties and interaction patterns in complex oscillator networks in the presence of noise. A striking finding is that noise leads to a general, one-to-one correspondence between the dynamical…
Piecewise diffusion Markov processes (PDifMPs) form a versatile class of stochastic hybrid systems that combine continuous diffusion processes with discrete event-driven dynamics, enabling flexible modelling of complex real-world hybrid…
In this study we put forth a modular approach for distilling hidden flow physics in discrete and sparse observations. To address functional expressiblity, a key limitation of the black-box machine learning methods, we have exploited the use…
Fueled in part by recent applications in neuroscience, the multivariate Hawkes process has become a popular tool for modeling the network of interactions among high-dimensional point process data. While evaluating the uncertainty of the…
We report new statistical time-series analysis tools providing significant improvements in the rapid, precision extraction of discrete state dynamics from large databases of experimental observations of molecular machines. By building…
Traditionally, Hawkes processes are used to model time--continuous point processes with history dependence. Here we propose an extended model where the self--effects are of both excitatory and inhibitory type and follow a Gaussian Process.…
Analytical work probability distributions for open classical systems are scarce; they can only be calculated in a few examples. In this work, I present a new method to derive such quantities for weakly driven processes in the overdamped…
The fluctuation-dissipation relation, a central result in non-equilibrium statistical physics, relates equilibrium fluctuations in a system to its linear response to external forces. Here we provide a direct experimental verification of…
Maximum Entropy is a powerful concept that entails a sharp separation between relevant and irrelevant variables. It is typically invoked in inference, once an assumption is made on what the relevant variables are, in order to estimate a…
The Hawkes process has garnered attention in recent years for its suitability to describe the behavior of online information cascades. Here, we present a fully tractable approach to analytically describe the distribution of the number of…
In this paper, we introduce a new class of processes which are diffusions with jumps driven by a multivariate nonlinear Hawkes process. Our goal is to study their long-time behavior. In the case of exponential memory kernels for the…
The volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, the volatility is unobservable…
In this work, several convergence results are established for nearly critical self-excited systems in which event arrivals are described by multivariate marked Hawkes point processes. Under some mild high-frequency assumptions, the rescaled…
We compare the Malliavin-Mancino and Cuchiero-Teichmann Fourier instantaneous estimators to investigate the impact of the Epps effect arising from asynchrony in the instantaneous estimates. We demonstrate the instantaneous Epps effect under…
We present a novel method for measuring the rate of periodic phenomena (e.g., rotation, flicker, and vibration), by an event camera, a device asynchronously reporting brightness changes at independently operating pixels with high temporal…
Positive feedback trading, which buys when prices rise and sells when prices fall, has long been criticized for being destabilizing as it moves prices away from the fundamentals. Motivated by the relationship between positive feedback…
Thanks to technological advances leading to near-continuous time observations, emerging multivariate point process data offer new opportunities for causal discovery. However, a key obstacle in achieving this goal is that many relevant…
We show that in periodically driven systems, along with the delta-peak at the driving frequency, the spectral density of fluctuations displays extra features. These can be peaks or dips with height quadratic in the driving amplitude, for…
Functional data analysis, which models data as realizations of random functions over a continuum, has emerged as a useful tool for time series data. Often, the goal is to infer the dynamic connections (or time-varying conditional…
Trade executions for major stocks come in bursts of activity, which can be partly attributed to the presence of self- and mutual excitations endogenous to the system. In this paper, we study transaction reports for five FTSE 100 stocks. We…