Related papers: Autocorrelation functions for point-process time s…
Investigating the relationship, particularly the lead-lag effect, between time series is a common question across various disciplines, especially when uncovering biological process. However, analyzing time series presents several…
We demonstrate that extremely rapid and weak periodic and non-periodic signals can easily be detected by using the autocorrelation of intensity as a function of time. We use standard radio-astronomical observations that have artificial…
When dealing with time series data, causal inference methods often employ structural vector autoregressive (SVAR) processes to model time-evolving random systems. In this work, we rephrase recursive SVAR processes with possible latent…
The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…
The momentum or velocity autocorrelation function C(t) for a tagged oscillator in a finite harmonic system decays like that of an infinite system for short times, but exhibits erratic behavior at longer time scales. We introduce the…
The convergence of a sequence of point processes with dependent points, defined by a symmetric function of iid high-dimensional random vectors, to a Poisson random measure is proved. This also implies the convergence of the joint…
The use of empirical characteristic functions for inference problems, including estimation in some special parametric settings and testing for goodness of fit, has a long history dating back to the 70s (see for example, Feuerverger and…
We study two-state (dichotomous, telegraph) random ergodic continuous-time processes with dynamics depending on their past. We take into account the history of process in an explicit form by introducing an integral non-local memory term…
A semi-analytic method is proposed for the generation of realizations of a multivariate process of a given linear correlation structure and marginal distribution. This is an extension of a similar method for univariate processes,…
The concept of a random process has been recently extended to graph signals, whereby random graph processes are a class of multivariate stochastic processes whose coefficients are matrices with a \textit{graph-topological} structure. The…
Established techniques for simulation and prediction with Gaussian process (GP) dynamics often implicitly make use of an independence assumption on successive function evaluations of the dynamics model. This can result in significant error…
Time-averaged autocorrelation functions of a dichotomous random process switching between 1 and 0 and governed by wide power law sojourn time distribution are studied. Such a process, called a L\'evy walk, describes dynamical behaviors of…
Whenever eye movements are measured, a central part of the analysis has to do with where subjects fixate, and why they fixated where they fixated. To a first approximation, a set of fixations can be viewed as a set of points in space: this…
We propose a new cross-correlation method that can recognize independent realizations of the same type of stochastic processes and can be used as a new kind of pattern recognition tool in biometrics, sensing, forensic, security and image…
We introduce a counting process to model the random occurrence in time of car traffic accidents, taking into account some aspects of the self-excitation typical of this phenomenon. By combining methods from probability and differential…
The production system (multidimensional object) is considered as a dynamic system with discrete time. Formalized: space (state of the object, control actions, goals, observed values, analytical estimates). Analytical estimates of the state…
Much of interesting complex biological behaviour arises from collective properties. Important information about collective behaviour lies in the time and space structure of fluctuations around average properties, and two-point correlation…
Detecting early warning signals in climatic time series is essential for anticipating critical transitions and tipping points. Common statistical indicators include increased variance and lag-one autocorrelation prior to bifurcation points.…
This paper presents a kriging method for spatial prediction of temporal intensity functions, for situations where a temporal point process is observed at different spatial locations. Assuming that several replications of the processes are…
Point process models have been used to analyze interaction event times on a social network, in the hope to provides valuable insights for social science research. However, the diagnostics and visualization of the modeling results from such…