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A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to…

An approach is proposed to determine structural shift in time-series assuming non-linear dependence of lagged values of dependent variable. Copulas are used to model non-linear dependence of time series components.

In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…

A class of multivariate periodic autoregressive models is proposed where coupling between time series is achieved through linear mean functions. Various response distributions with quadratic mean-variance relationships fit into the…

This paper studies some temporal dependence properties and addresses the issue of parametric estimation for a class of state-dependent autoregressive models for nonlinear time series in which we assume a stochastic autoregressive…

We prove the non-uniqueness theorem for the chronological products of a gauge model. We use a cohomological language where the cochains are chronological products, gauge invariance means a cocycle restriction and coboundaries are…

This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for…

Ordered sequences of univariate or multivariate regressions provide statistical models for analysing data from randomized, possibly sequential interventions, from cohort or multi-wave panel studies, but also from cross-sectional or…

Uncertainty quantification of predictive models is crucial in decision-making problems. Conformal prediction is a general and theoretically sound answer. However, it requires exchangeable data, excluding time series. While recent works…

We consider two weakly coupled systems and adopt a perturbative approach based on the Ruelle response theory to study their interaction. We propose a systematic way to parametrize the effect of the coupling as a function of only the…

We studied the effects of time correlation of subsequent patterns on the convergence of on-line learning by a feedforward neural network with backpropagation algorithm. By using chaotic time series as sequences of correlated patterns, we…

In this paper we employ methods from Statistical Mechanics to model temporal correlations in time series. We put forward a methodology based on the Maximum Entropy principle to generate ensembles of time series constrained to preserve part…

This paper considers the problem of controlling a piecewise continuously differentiable system subject to time-varying uncertainties. The uncertainties are decomposed into a time-invariant, linearly-parameterized portion and a time-varying…

Change point detection in time series aims to identify moments when the probability distribution of time series changes. It is widely applied in many areas, such as human activity sensing and medical science. In the context of multivariate…

Generalized linear and additive models are very efficient regression tools but the selection of relevant terms becomes difficult if higher order interactions are needed. In contrast, tree-based methods also known as recursive partitioning…

In multivariate time series systems, lead-lag relationships reveal dependencies between time series when they are shifted in time relative to each other. Uncovering such relationships is valuable in downstream tasks, such as control,…

Measuring the statistical dependence between observed signals is a primary tool for scientific discovery. However, biological systems often exhibit complex non-linear interactions that currently cannot be captured without a priori knowledge…

Despite the excelling performance of machine learning models, understanding their decisions remains a long-standing goal. Although commonly used attribution methods from explainable AI attempt to address this issue, they typically rely on…

Causal decomposition depicts a cause-effect relationship that is not based on the concept of prediction, but based on the phase dependence of time series. It has been validated in both stochastic and deterministic systems and is now…

Discrimination between non-stationarity and long-range dependency is a difficult and long-standing issue in modelling financial time series. This paper uses an adaptive spectral technique which jointly models the non-stationarity and…