Related papers: Autoregressive Models for Variance Matrices: Stati…
This paper addresses the prediction of stationary functional time series. Existing contributions to this problem have largely focused on the special case of first-order functional autoregressive processes because of their technical…
In many applications, data are observed as matrices with temporal dependence. Matrix-variate time series modeling is a new branch of econometrics. Although stylized facts in several fields, the existing models do not account for regime…
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)…
We consider a class of vector autoregressive models with banded coefficient matrices. The setting represents a type of sparse structure for high-dimensional time series, though the implied autocovariance matrices are not banded. The…
We propose a new class of univariate nonstationary time series models, using the framework of modulated time series, which is appropriate for the analysis of rapidly-evolving time series as well as time series observations with missing…
We propose in this work a new family of kernels for variable-length time series. Our work builds upon the vector autoregressive (VAR) model for multivariate stochastic processes: given a multivariate time series x, we consider the…
This work studies the problem of modeling visual processes by leveraging deep generative architectures for learning linear, Gaussian representations from observed sequences. We propose a joint learning framework, combining a vector…
In this paper, we give a AR$(1)$ type of characterization covering all multivariate strictly stationary processes indexed by the set of integers. Consequently, we derive continuous time algebraic Riccati equations for the parameter matrix…
Modeling nonstationary processes is of paramount importance to many scientific disciplines including environmental science, ecology, and finance, among others. Consequently, flexible methodology that provides accurate estimation across a…
When considering the problem of forecasting a continuous-time stochastic process over an entire time-interval in terms of its recent past, the notion of Autoregressive Hilbert space processes (ARH) arises. This model can be seen as a…
We consider the estimation of the transition matrix in the high-dimensional time-varying vector autoregression (TV-VAR) models. Our model builds on a general class of locally stationary VAR processes that evolve smoothly in time. We propose…
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 propose a recurrent neural network for a "model-free" simulation of a dynamical system with unknown parameters without prior knowledge. The deep learning model aims to jointly learn the nonlinear time marching operator and the effects of…
Predictive linear and nonlinear models based on kernel machines or deep neural networks have been used to discover dependencies among time series. This paper proposes an efficient nonlinear modeling approach for multiple time series, with a…
We address the problem of learning graphical models which correspond to high dimensional autoregressive stationary stochastic processes. A graphical model describes the conditional dependence relations among the components of a stochastic…
As evidenced by various recent and significant papers within the frequentist literature, along with numerous applications in macroeconomics, genomics, and neuroscience, there continues to be substantial interest to understand the…
This study delves into the domain of dynamical systems, specifically the forecasting of dynamical time series defined through an evolution function. Traditional approaches in this area predict the future behavior of dynamical systems by…
In this paper, we consider a model called CHARME (Conditional Heteroscedastic Autoregressive Mixture of Experts), a class of generalized mixture of nonlinear nonparametric AR-ARCH time series. Under certain Lipschitz-type conditions on the…
Nonlinear stochastic modeling is useful for describing complex engineering systems. Meanwhile, neuromorphic (brain-inspired) computing paradigms are developing to tackle tasks that are challenging and resource intensive on digital…
Recent advances in the estimation of deep directed graphical models and recurrent networks let us contribute to the removal of a blind spot in the area of probabilistc modelling of time series. The proposed methods i) can infer distributed…