Related papers: Some Probabilistic and Statistical Properties of a…

We study a linear recursion with random Markov-dependent coefficients. In a "regular variation in, regular variation out" setup we show that its stationary solution has a multivariate regularly varying distribution. This extends results…

Real-world data often exhibits sequential dependence, across diverse domains such as human behavior, medicine, finance, and climate modeling. Probabilistic methods capture the inherent uncertainty associated with prediction in these…

In this study, we propose a test for the coefficient randomness in autoregressive models where the autoregressive coefficient is local to unity, which is empirically relevant given the results of earlier studies. Under this specification,…

Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is…

We study discrete linear divergence-form operators with random coefficients, also known as the random conductance model. We assume that the conductances are bounded, independent and stationary; the law of a conductance may depend on the…

A family of continuous-time generalized autoregressive conditionally heteroscedastic processes, generalizing the $\operatorname {COGARCH}(1,1)$ process of Kl\"{u}ppelberg, Lindner and Maller [J. Appl. Probab. 41 (2004) 601--622], is…

Divergence-form operators with stationary random coefficients homogenize over large scales. We investigate the effect of certain perturbations of the medium on the homogenized coefficients. The perturbations that we consider are rare at the…

Strict stationarity is a common assumption used in the time series literature in order to derive asymptotic distributional results for second-order statistics, like sample autocovariances and sample autocorrelations. Focusing on weak…

We show that the class of conditional distributions satisfying the coarsening at random (CAR) property for discrete data has a simple and robust algorithmic description based on randomized uniform multicovers: combinatorial objects…

In this paper, we introduce the first-order integer-valued autoregressive (INAR(1)) model, with Poisson-Lindley innovations based on power series thinning operator. Some mathematical features of this process are given and estimating the…

We consider random coefficient autoregressive models of infinite order (AR($\infty$)) under the assumption of non-negativity of the coefficients. We develop novel methods yielding sufficient or necessary conditions for finiteness of…

We derive generalization error bounds for stationary univariate autoregressive (AR) models. We show that imposing stationarity is enough to control the Gaussian complexity without further regularization. This lets us use structural risk…

Many natural phenomena can be described by power-laws. A closer look at various experimental data reveals more or less significant deviations from a 1/f spectrum. We exemplify such cases with phenomena offered by molecular biology, cell…

The first author introduced a sequence of polynomials (\cite{8}, sequence A174531) defined recursively. One of the main results of this study is proof of the integrality of its coefficients.

We discuss existence and uniqueness of stationary and ergodic nonlinear autoregressive processes when exogenous regressors are incorporated in the dynamic. To this end, we consider the convergence of the backward iterations of dependent…

This paper studies theory and inference of an observation-driven model for time series of counts. It is assumed that the observations follow a Poisson distribution conditioned on an accompanying intensity process, which is equipped with a…

Contemporary time series data often feature objects connected by a social network that naturally induces temporal dependence involving connected neighbours. The network vector autoregressive model is useful for describing the influence of…

We introduce a general class of autoregressive models for studying the dynamic of multivariate binary time series with stationary exogenous covariates. Using a high-level set of assumptions, we show that existence of a stationary path for…

Iterative imputation, in which variables are imputed one at a time each given a model predicting from all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modeling…

Stationary processes have been extensively studied in the literature. Their applications include modeling and forecasting numerous real life phenomena such as natural disasters, sales and market movements. When stationary processes are…