相关论文: On the novel geometric and negative binomial INAR(…

Most of the stationary first-order autoregressive integer-valued (INAR(1)) models were developed for a given thinning operator using either the forward approach or the backward approach. In the forward approach the marginal distribution of…

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 introduce a two-parameter expectation thinning operator based on a linear fractional probability generating function. The operator is then used to define a first-order integer-valued autoregressive \inar1 process. Distributional…

INteger Auto-Regressive (INAR) processes are usually defined by specifying the innovations and the operator, which often leads to difficulties in deriving marginal properties of the process. In many practical situations, a major modeling…

In this paper, we present a fractional decomposition of the probability generating function of the innovation process of the first-order non-negative integer-valued autoregressive [INAR(1)] process to obtain the corresponding probability…

A popular and flexible time series model for counts is the generalized integer autoregressive process of order $p$, GINAR($p$). These Markov processes are defined using thinning operators evaluated on past values of the process along with a…

An extension of the RINAR(1) process for modelling discrete-time dependent counting processes is considered. The model RINAR(p) investigated here is a direct and natural extension of the real AR(p) model. Compared to classical INAR(p)…

Integer-valued time series models have been a recurrent theme considered in many papers in the last three decades, but only a few of them have dealt with models on $\mathbb Z$ (that is, including both negative and positive integers). Our…

In this paper, a new bivariate random coefficient integer-valued autoregressive process based on modified negative binomial operator with dependent innovations is proposed. Basic probabilistic and statistical properties of this model are…

In this paper, we introduce a new first-order mixture integer-valued threshold autoregressive process, based on the binomial and negative binomial thinning operators. Basic probabilistic and statistical properties of this model are…

Strictly stationary INAR(1) ("integer-valued autoregressive processes of order 1") with Poisson innovations are "interlaced rho-mixing".

In the fields of sociology and economics, the modeling of matrix-variate integervalued time series is urgent. However, no prior studies have addressed the modeling of such data. To address this topic, this paper proposes a novel…

An inhomogeneous first--order integer--valued autoregressive (INAR(1)) process is investigated, where the autoregressive type coefficient slowly converges to one. It is shown that the process converges weakly to a Poisson or a compound…

In this article, we introduce and study a one sided tempered stable first order autoregressive model called TAR(1). Under the assumption of stationarity of the model, the marginal probability density function of the error term is found. It…

We introduce a neural network architecture to solve inverse problems linked to a one-dimensional integral operator. This architecture is built by unfolding a forward-backward algorithm derived from the minimization of an objective function…

In this article we discuss the convergence of first order operators on a thickened graph (a graph-like space) towards a similar operator on the underlying metric graph. On the graph-like space, the first order operator is of the form…

Real count data time series often show the phenomenon of the underdispersion and overdispersion. In this paper, we develop two extensions of the first-order integer-valued autoregressive process with Poisson innovations, based on binomial…

Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…

A new integer--valued autoregressive process (INAR) with Generalised Lagrangian Katz (GLK) innovations is defined. This process family provides a flexible modelling framework for count data, allowing for under and over--dispersion,…

The first-order autoregressive process, AR (1), has been widely used and implemented in time series analysis. Different estimation methods have been employed in order to estimate the autoregressive parameter. This article focuses on…