Related papers: Inverse covariance operators of multivariate nonst…

We consider estimation of covariance matrices and their inverses (a.k.a. precision matrices) for high-dimensional stationary and locally stationary time series. In the latter case the covariance matrices evolve smoothly in time, thus…

In this paper, we consider the nonstationary matrix-valued time series with common stochastic trends. Unlike the traditional factor analysis which flattens matrix observations into vectors, we adopt a matrix factor model in order to fully…

Multivariate spatial-statistical models are often used when modeling environmental and socio-demographic processes. The most commonly used models for multivariate spatial covariances assume both stationarity and symmetry for the…

The functional linear model extends the notion of linear regression to the case where the response and covariates are iid elements of an infinite dimensional Hilbert space. The unknown to be estimated is a Hilbert-Schmidt operator, whose…

Stationarity is a very common assumption in time series analysis. A vector autoregressive process is stationary if and only if the roots of its characteristic equation lie outside the unit circle, constraining the autoregressive coefficient…

The purpose of this paper is to propose a time-varying vector autoregressive model (TV-VAR) for forecasting multivariate time series. The model is casted into a state-space form that allows flexible description and analysis. The volatility…

Vector autoregressive (VAR) models have become a staple in the analysis of multivariate time series and are formulated in the time domain as difference equations, with an implied covariance structure. In many contexts, it is desirable to…

We develop an estimator for the high-dimensional covariance matrix of a locally stationary process with a smoothly varying trend and use this statistic to derive consistent predictors in non-stationary time series. In contrast to the…

The salient properties of large empirical covariance and correlation matrices are studied for three datasets of size 54, 55 and 330. The covariance is defined as a simple cross product of the returns, with weights that decay logarithmically…

Statistical analysis of high-dimensional functional times series arises in various applications. Under this scenario, in addition to the intrinsic infinite-dimensionality of functional data, the number of functional variables can grow with…

We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order of magnitude is derived for spectral radius of sample covariance matrices. We also consider a thresholded covariance matrix…

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…

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…

This paper deals with the time-varying high dimensional covariance matrix estimation. We propose two covariance matrix estimators corresponding with a time-varying approximate factor model and a time-varying approximate characteristic-based…

Second-order characteristics including covariance and spectral density functions are fundamentally important for both statistical applications and theoretical analysis in functional time series. In the high-dimensional setting where the…

In modeling multivariate time series, it is important to allow time-varying smoothness in the mean and covariance process. In particular, there may be certain time intervals exhibiting rapid changes and others in which changes are slow. If…

In multivariate time series, the estimation of the covariance matrix of the observation innovations plays an important role in forecasting as it enables the computation of the standardized forecast error vectors as well as it enables the…

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…

Recent works have shown an interest in investigating the frequentist asymptotic properties of Bayesian procedures for high-dimensional linear models under sparsity constraints. However, there exists a gap in the literature regarding…

Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…