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We introduce a recursive algorithm of conveniently general form for estimating the coefficient of a moving average model of order one and obtain convergence results for both correct and misspecified MA(1) models. The algorithm encompasses…
We propose a new class of models specifically tailored for spatio-temporal data analysis. To this end, we generalize the spatial autoregressive model with autoregressive and heteroskedastic disturbances, i.e. SARAR(1,1), by exploiting the…
We propose two novel ways of introducing dependence among Poisson counts through the use of latent variables in a three levels hierarchical model. Marginal distributions of the random variables of interest are Poisson with strict…
In this article, we discuss some geometric infinitely divisible (gid) random variables using the Laplace exponents which are Bernstein functions and study their properties. The distributional properties and limiting behavior of the…
A new mixture autoregressive model based on Student's $t$-distribution is proposed. A key feature of our model is that the conditional $t$-distributions of the component models are based on autoregressions that have multivariate…
In this paper, we consider the normalized least squares estimator of the parameter in a mildly stationary first-order autoregressive (AR(1)) model with dependent errors which are modeled as a mildly stationary AR(1) process. By martingale…
We study a fixed-$T$ panel data logit model for ordered outcomes that accommodates fixed effects and state dependence. We provide identification results for the autoregressive parameter, regression coefficients, and the threshold parameters…
Autoregressive models (ARMs) have become the workhorse for sequence generation tasks, since many problems can be modeled as next-token prediction. While there appears to be a natural ordering for text (i.e., left-to-right), for many data…
Condition numbers of random polynomial systems have been widely studied in the literature under certain coefficient ensembles of invariant type. In this note we introduce a method that allows us to study these numbers for a broad family of…
This paper proposes a linear categorical random coefficient model, in which the random coefficients follow parametric categorical distributions. The distributional parameters are identified based on a linear recurrence structure of moments…
Strictly stationary INAR(1) ("integer-valued autoregressive processes of order 1") with Poisson innovations are "interlaced rho-mixing".
Given an autoregressive process X of order p (i.e. X_n = a_1 X_{n-1} + ...+ a_p X_{n_p} + Y_n where the random variables Y_1, Y_2, ... are i.i.d.), we study the asymptotic behaviour of the probability that the process does not exceed a…
In this contribution we introduce weakly locally stationary time series through the local approximation of the non-stationary covariance structure by a stationary one. This allows us to define autoregression coefficients in a non-stationary…
This paper considers the quantile regression approach for partially linear spatial autoregressive models with possibly varying coefficients. B-spline is employed for the approximation of varying coefficients. The instrumental variable…
This paper introduces a periodic multivariate Poisson autoregression with potentially infinite memory, with a special focus on the network setting. Using contraction techniques, we study the stability of such a process and provide upper…
We propose a stochastic model for claims reserving that captures dependence along development years within a single triangle. This dependence is of autoregressive form of order $p$ and is achieved through the use of latent variables. We…
A novel first-order moving-average model for analyzing time series observed at irregularly spaced intervals is introduced. Two definitions are presented, which are equivalent under Gaussianity. The first one relies on normally distributed…
Conditions for positive and polynomial recurrence have been proposed for a class of reliability models of two elements with transitions from working state to failure and back. As a consequence, uniqueness of stationary distribution of the…
This paper deals with the maximum likelihood estimator for the mean-reverting parameter of a first order autoregressive models with exogenous variables, which are stationary Gaussian noises (Colored noise). Using the method of the Laplace…
Conditional inference on arbitrary subsets of variables is a core problem in probabilistic inference with important applications such as masked language modeling and image inpainting. In recent years, the family of Any-Order Autoregressive…