Related papers: Continuous-time models with an autoregressive stru…

Vector autoregressive models characterize a variety of time series in which linear combinations of current and past observations can be used to accurately predict future observations. For instance, each element of an observation vector…

Tiny Recursive Models (TRMs) have recently demonstrated remarkable performance on ARC-AGI, showing that very small models can compete against large foundation models through a two-step refinement mechanism that updates an internal reasoning…

We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…

The thinning-based integer-valued autoregressive moving-average (INARMA) models are popular for count time series. Recently, types of INARMA models have also been developed for count random fields, i.e., for spatial count data located on a…

It is known that input-output approaches based on scaled small-gain theorems with constant $D$-scalings and integral linear constraints are non-conservative for the analysis of some classes of linear positive systems interconnected with…

In a recurrent setting, conventional approaches to neural architecture search find and fix a general model for all data samples and time steps. We propose a novel algorithm that can dynamically search for the structure of cells in a…

We propose a novel cointegrated autoregressive model for matrix-valued time series, with bi-linear cointegrating vectors corresponding to the rows and columns of the matrix data. Compared to the traditional cointegration analysis, our…

In the copula-based approach to univariate time series modeling, the finite dimensional temporal dependence of a stationary time series is captured by a copula. Recent studies investigate how copula-based time series models can be…

Recently, matrix-valued time series data have attracted significant attention in the literature with the recognition of threshold nonlinearity representing a significant advance. However, given the fact that a matrix is a two-array…

Mechanisms are elucidated underlying the existence of dynamical systems whose generic solutions approach asymptotically (at large time) isochronous evolutions: all their dependent variables tend asymptotically to functions periodic with the…

Designing a universal policy architecture that performs well across diverse robots and task configurations remains a key challenge. In this work, we address this by representing robot actions as sequential data and generating actions…

A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…

In this paper we study reflected backward stochastic differential equations with a continuous, linear growth coefficient and two barriers which belong to L^2. We prove that there exists at least by penalization method.

We study the problem of modeling and inference for spatio-temporal count processes. Our approach uses parsimonious parameterisations of multivariate autoregressive count time series models, including possible regression on covariates. We…

This paper focuses on the dynamical properties of delayed complex balanced systems. We first study the relationship between the stoichiometric compatibility classes of delayed and non-delayed systems. Using this relation we give another way…

A class of multivariate periodic autoregressive models is proposed where coupling between time series is achieved through linear mean functions. Various response distributions with quadratic mean-variance relationships fit into the…

When dealing with time series data, causal inference methods often employ structural vector autoregressive (SVAR) processes to model time-evolving random systems. In this work, we rephrase recursive SVAR processes with possible latent…

This paper investigates the modeling of an important class of degradation data, which are collected from a spatial domain over time; for example, the surface quality degradation. Like many existing time-dependent stochastic degradation…

In this paper, we introduce a new method for study on backward stochastic differential equations with stopping time as time horizon. And using this, we show that some results on backward stochastic differential equations with constant time…

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…