Related papers: Stochastic Equicontinuity in Nonlinear Time Series…

This paper is a note on the use of Bayesian nonparametric mixture models for continuous time series. We identify a key requirement for such models, and then establish that there is a single type of model which meets this requirement. As it…

We propose an informal test for stationarity in a time series which checks for the compatibility of nonlinear approximations to the dynamics made in different segments of the sequence. The segments are compared directly, rather than via…

This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely…

In this paper we consider multivariate time series obtained as solution to multidimensional nonlinear stochastic difference equations whose coefficients are allowed to be locally degenerate and to present discontinuities. We provide simple…

Probabilistic forecasting of multivariate time series is essential for various downstream tasks. Most existing approaches rely on the sequences being uniformly spaced and aligned across all variables. However, real-world multivariate time…

Stochastic dynamical systems often contain nonlinearities which make it hard to compute probability density functions or statistical moments of these systems. For the moment computations, nonlinearities in the dynamics lead to unclosed…

We introduce a statistical method to detect nonlinearity and nonstationarity in time series, that works even for short sequences and in presence of noise. The method has a discrimination power similar to that of the most advanced estimators…

We propose a novel method applied to extrasolar planetary dynamics to describe the system stability. The observations in this field serve the measurements mainly of radial velocity, transit time, and/or celestial position. These scalar time…

The family of U-statistics plays a fundamental role in statistics. This paper proves a novel exponential inequality for U-statistics under the time series setting. Explicit mixing conditions are given for guaranteeing fast convergence, the…

We derive sufficient conditions for the solvability of the observer design problem for a wide class of nonlinear time-varying systems, including those having triangular structure. We establish that, under weaker assumptions than those…

This article discusses recent developments in the literature of quantile time series models in the cases of stationary and nonstationary underline stochastic processes.

This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…

Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…

A binary fluid mixture in contact with lateral particle reservoirs is considered. By imposing different particle concentrations in these reservoirs, the system can be maintained under controlled non-equilibrium conditions. Previous…

We study the persistence in a class of continuous stochastic processes that are stationary only under integer shifts of time. We show that under certain conditions, the persistence of such a continuous process reduces to the persistence of…

The current algorithms are based on linear model, for example, Precision Time Protocol (PTP) which requires frequent synchronization in order to handle the effects of clock frequency drift. This paper introduces a nonlinear approach to…

Financial markets are prominent examples for highly non-stationary systems. Sample averaged observables such as variances and correlation coefficients strongly depend on the time window in which they are evaluated. This implies severe…

Parameter estimation in a class of heteroscedastic time series models is investigated. The existence of conditional least-squares and conditional likelihood estimators is proved. Their consistency and their asymptotic normality are…

This paper deals with a general class of observation-driven time series models with a special focus on time series of counts. We provide conditions under which there exist strict-sense stationary and ergodic versions of such processes. The…

This article shows how to specify and construct a discrete, stochastic, continuous-time model specifically for ecological systems. The model is more broad than typical chemical kinetics models in two ways. First, using time-dependent hazard…