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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…

Statistics Theory · Mathematics 2025-09-10 Nuo Xu , Kai Yang , Fukang Zhu

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…

Methodology · Statistics 2024-02-06 Pashmeen Kaur , Peter F. Craigmile

We consider the problem of defining and fitting models of autoregressive time series of probability distributions on a compact interval of $\mathbb{R}$. An order-$1$ autoregressive model in this context is to be understood as a Markov…

Methodology · Statistics 2023-03-17 Laya Ghodrati , Victor M. Panaretos

It is known that backward iterations of independent copies of a contractive random Lipschitz function converge almost surely under mild assumptions. By a sieving (or thinning) procedure based on adding to the functions time and space…

Probability · Mathematics 2020-03-25 Alexander Marynych , Ilya Molchanov

We obtain the rate of growth of long strange segments and the rate of decay of infinite horizon ruin probabilities for a class of infinite moving average processes with exponentially light tails. The rates are computed explicitly. We show…

Probability · Mathematics 2010-10-18 Souvik Ghosh , Gennady Samorodnitsky

We consider maximum likelihood estimation for both causal and noncausal autoregressive time series processes with non-Gaussian $\alpha$-stable noise. A nondegenerate limiting distribution is given for maximum likelihood estimators of the…

Statistics Theory · Mathematics 2009-08-14 Beth Andrews , Matthew Calder , Richard A. Davis

In this work, we consider the class of multi-state autoregressive processes that can be used to model non-stationary time-series of interest. In order to capture different autoregressive (AR) states underlying an observed time series, it is…

Machine Learning · Statistics 2015-10-13 Jie Ding , Mohammad Noshad , Vahid Tarokh

A graph generative model defines a distribution over graphs. One type of generative model is constructed by autoregressive neural networks, which sequentially add nodes and edges to generate a graph. However, the likelihood of a graph under…

Machine Learning · Statistics 2021-06-15 Xiaohui Chen , Xu Han , Jiajing Hu , Francisco J. R. Ruiz , Liping Liu

Stochastic processes with long memories, known as long memory processes, are ubiquitous in various science and engineering problems. Superposing Markovian stochastic processes generates a non-Markovian long memory process serving as…

Probability · Mathematics 2025-11-24 Hidekazu Yoshioka

Information storage, reflecting the capability of a dynamical system to keep predictable information during its evolution over time, is a key element of intrinsic distributed computation, useful for the description of the dynamical…

Empirical likelihood method has been applied to short-memory time series models by Monti (1997) through the Whittle's estimation method. Yau (2012) extended this idea to long-memory time series models. Asymptotic distributions of the…

Methodology · Statistics 2016-04-22 Ramadha D. Piyadi Gamage , Wei Ning , Arjun K. Gupta

State of the art large language models rely on randomization to respond to a prompt. As an immediate consequence, a model may respond differently to the same prompt if asked multiple times. In this work, we argue that the evaluation and…

In order to scale standard Gaussian process (GP) regression to large-scale datasets, aggregation models employ factorized training process and then combine predictions from distributed experts. The state-of-the-art aggregation models,…

Machine Learning · Statistics 2018-06-05 Haitao Liu , Jianfei Cai , Yi Wang , Yew-Soon Ong

In this paper we suggest two continuous-time models which exhibit an autoregressive structure. We obtain existence and uniqueness results and study the structure of the solution processes. One of the models, which corresponds to general…

Probability · Mathematics 2018-11-13 Andreas Basse-O'Connor , Mikkel Slot Nielsen , Jan Pedersen , Victor Rohde

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…

Methodology · Statistics 2020-07-27 Josemar Rodrigues , Marcelo Bourguignon , Manoel Santos-Neto , N. Balakrishnan

We consider empirical multi-dimensional Rare Events Point Processes that keep track both of the time occurrence of extremal observations and of their severity, for stochastic processes arising from a dynamical system, by evaluating a given…

Dynamical Systems · Mathematics 2017-09-19 Ana Cristina Moreira Freitas , Jorge Milhazes Freitas , Mário Magalhães

Some convergence results on the kernel density estimator are proven for a class of linear processes with cyclical effects. In particular we extend the results of Ho and Hsing (1996a) and Mielniczuk (1997) to the stationary processes for…

Statistics Theory · Mathematics 2011-04-18 Mohamedou Ould Haye , Anne Philippe

Contemporary time series analysis has seen more and more tensor type data, from many fields. For example, stocks can be grouped according to Size, Book-to-Market ratio, and Operating Profitability, leading to a 3-way tensor observation at…

Methodology · Statistics 2021-10-05 Zebang Li , Han Xiao

We introduce a class of discrete time stationary trawl processes taking real or integer values and written as sums of past values of independent `seed' processes on shrinking intervals (`trawl heights'). Related trawl processes in…

Probability · Mathematics 2016-10-18 Paul Doukhan , Silvia Lopes , Adam Jakubowski , Donatas Surgailis

We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…

Statistical Mechanics · Physics 2015-05-13 N. R. Moloney , J. Davidsen