Related papers: Autoregressive Models for Variance Matrices: Stati…

High-dimensional vector autoregressive (VAR) models have numerous applications in fields such as econometrics, biology, climatology, among others. While prior research has mainly focused on linear VAR models, these approaches can be…

The autoregressive process of order $p$ (AR($p$)) is a central model in time series analysis. A Bayesian approach requires the user to define a prior distribution for the coefficients of the AR($p$) model. Although it is easy to write down…

Modeling correlation (and covariance) matrices can be challenging due to the positive-definiteness constraint and potential high-dimensionality. Our approach is to decompose the covariance matrix into the correlation and variance matrices…

We consider a short rate model, driven by a stochastic process on the cone of positive semidefinite matrices. We derive sufficient conditions ensuring that the model replicates normal, inverse or humped yield curves.

Graph-based methods for signal processing have shown promise for the analysis of data exhibiting irregular structure, such as those found in social, transportation, and sensor networks. Yet, though these systems are often dynamic,…

Time series of matrix-valued data are increasingly available in various areas including economics, finance, social science, among others. These data may shed light on the inter-dynamical relationships between two sets of attributes, for…

WISDoM (Wishart Distributed Matrices) is a new framework for the quantification of deviation of symmetric positive-definite matrices associated to experimental samples, like covariance or correlation matrices, from expected ones governed by…

Among other uses, neural networks are a powerful tool for solving deterministic and Bayesian inverse problems in real-time, where variational autoencoders, a specialized type of neural network, enable the Bayesian estimation of model…

High-dimensional vector autoregressive (VAR) models are important tools for the analysis of multivariate time series. This paper focuses on high-dimensional time series and on the different regularized estimation procedures proposed for…

A Bayesian procedure is developed for multivariate stochastic volatility, using state space models. An autoregressive model for the log-returns is employed. We generalize the inverted Wishart distribution to allow for different correlation…

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…

We develop a new methodology for forecasting matrix-valued time series with historical matrix data and auxiliary vector time series data. We focus on a time series of matrices defined on a static 2-D spatial grid and an auxiliary time…

Several disciplines, such as econometrics, neuroscience, and computational psychology, study the dynamic interactions between variables over time. A Bayesian nonparametric model known as the Wishart process has been shown to be effective in…

Count-valued time series data are routinely collected in many application areas. We are particularly motivated to study the count time series of daily new cases, arising from COVID-19 spread. We propose two Bayesian models, a time-varying…

In this paper, non-linear time series models are used to describe volatility in financial time series data. To describe volatility, two of the non-linear time series are combined into form TAR (Threshold Auto-Regressive Model) with AARCH…

While much work has explored probabilistic graphical models for independent data, less attention has been paid to time series. The goal in this setting is to determine conditional independence relations between entire time series, which for…

Autoregressive (AR) models have been the dominating approach to conditional sequence generation, but are suffering from the issue of high inference latency. Non-autoregressive (NAR) models have been recently proposed to reduce the latency…

We study the problem of learning the support of transition matrix between random processes in a Vector Autoregressive (VAR) model from samples when a subset of the processes are latent. It is well known that ignoring the effect of the…

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…

Dynamic multilayer networks arise in many applications where multiple types of relations among a common set of nodes evolve over time. Existing approaches often assume temporal independence, focus on single-layer networks or impose…