Related papers: Autoregressive Models for Variance Matrices: Stati…
Multivariate network time series are ubiquitous in modern systems, yet existing network autoregressive models typically treat nodes as scalar processes, ignoring cross-variable spillovers. To capture these complex interactions without the…
We prove a large deviations principle for the class of multidimensional affine stochastic volatility models considered in (Gourieroux, C. and Sufana, R., J. Bus. Econ. Stat., 28(3), 2010), where the volatility matrix is modelled by a…
We review autoregressive models for the analysis of multivariate count time series. In doing so, we discuss the choice of a suitable distribution for a vectors of count random variables. This review focus on three main approaches taken for…
Estimating hidden processes from non-linear noisy observations is particularly difficult when the parameters of these processes are not known. This paper adopts a machine learning approach to devise variational Bayesian inference for such…
We present a bivariate vector valued discrete autoregressive model of order $1$ (BDAR($1$)) for discrete time series. The BDAR($1$) model assumes that each time series follows its own univariate DAR($1$) model with dependent random…
Multivariate $\operatorname {COGARCH}(1,1)$ processes are introduced as a continuous-time models for multidimensional heteroskedastic observations. Our model is driven by a single multivariate L\'{e}vy process and the latent time-varying…
The concept of a random process has been recently extended to graph signals, whereby random graph processes are a class of multivariate stochastic processes whose coefficients are matrices with a \textit{graph-topological} structure. The…
This article proposes methods to model nonstationary temporal graph processes. This corresponds to modelling the observation of edge variables (relationships between objects) indicating interactions between pairs of nodes (or objects)…
We propose a Weighted Autoregressive Varying gatE (WAVE) attention mechanism equipped with both Autoregressive (AR) and Moving-average (MA) components. It can adapt to various attention mechanisms, enhancing and decoupling their ability to…
This paper presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error…
In this work we introduce the class of unit-Weibull Autoregressive Moving Average models for continuous random variables taking values in $(0,1)$. The proposed model is an observation driven one, for which, conditionally on a set of…
This work deals with the simulation of Wishart processes and affine diffusions on positive semidefinite matrices. To do so, we focus on the splitting of the infinitesimal generator, in order to use composition techniques as Ninomiya and…
Multivariate dynamic time series models are widely encountered in practical studies, e.g., modelling policy transmission mechanism and measuring connectedness between economic agents. To better capture the dynamics, this paper proposes a…
The Wishart model of random covariance or correlation matrices continues to find ever more applications as the wealth of data on complex systems of all types grows. The heavy tails often encountered prompt generalizations of the Wishart…
Many deep neural networks have been used to solve Ising models, including autoregressive neural networks, convolutional neural networks, recurrent neural networks, and graph neural networks. Learning a probability distribution of energy…
Our goal is to estimate causal interactions in multivariate time series. Using vector autoregressive (VAR) models, these can be defined based on non-vanishing coefficients belonging to respective time-lagged instances. As in most cases a…
In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…
Paradoxically, while the assumptions of second-order stationarity and isotropy appear outdated in light of modern spatial data, they remain remarkably robust in practice, as nonstationary methods often provide marginal improvements in…
We introduce a Gaussian process-based model for handling of non-stationarity. The warping is achieved non-parametrically, through imposing a prior on the relative change of distance between subsequent observation inputs. The model allows…
Motivated by the proliferation of extensive macroeconomic and health datasets necessitating accurate forecasts, a novel approach is introduced to address Vector Autoregressive (VAR) models. This approach employs the global-local…