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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…

Statistics Theory · Mathematics 2017-10-03 Xin Ding , Ziyi Qiu , Xiaohui Chen

For time series with long-range temporal dependence, inference for covariance and precision matrices is non-trivial. We propose a Berry-Esseen type Gaussian approximation result that gives a finite-sample bound for the Kolmogorov distance…

Statistics Theory · Mathematics 2026-04-20 Percy S. Zhai , Mladen Kolar , Wei Biao Wu

The goal of this paper is to obtain expectation bounds for the deviation of large sample autocovariance matrices from their means under weak data dependence. While the accuracy of covariance matrix estimation corresponding to independent…

Statistics Theory · Mathematics 2019-05-27 Fang Han , Yicheng Li

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…

Statistics Theory · Mathematics 2022-01-14 Qin Fang , Shaojun Guo , Xinghao Qiao

In this paper, we consider the estimation and inference of precision matrices of a rich class of locally stationary and nonlinear time series assuming that only one realization of the time series is observed. Using a Cholesky decomposition…

Statistics Theory · Mathematics 2019-08-15 Xiucai Ding , Zhou Zhou

Precision matrices play important roles in many practical applications. Motivated by temporally dependent multivariate data in modern social and scientific studies, we consider the statistical inference of precision matrices for…

Methodology · Statistics 2018-12-21 Jinyuan Chang , Yumou Qiu , Qiwei Yao , Tao Zou

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…

Methodology · Statistics 2008-02-04 K. Triantafyllopoulos

We propose a pointwise inference algorithm for high-dimensional linear models with time-varying coefficients. The method is based on a novel combination of the nonparametric kernel smoothing technique and a Lasso bias-corrected ridge…

Methodology · Statistics 2017-03-17 Xiaohui Chen , Yifeng He

Estimating large covariance and precision matrices are fundamental in modern multivariate analysis. The problems arise from statistical analysis of large panel economics and finance data. The covariance matrix reveals marginal correlations…

Methodology · Statistics 2015-04-17 Jianqing Fan , Yuan Liao , Han Liu

The vector autoregressive (VAR) model is a powerful tool in modeling complex time series and has been exploited in many fields. However, fitting high dimensional VAR model poses some unique challenges: On one hand, the dimensionality,…

Machine Learning · Statistics 2014-10-30 Fang Han , Huanran Lu , Han Liu

The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the…

Computation · Statistics 2017-12-06 Per Sidén , Finn Lindgren , David Bolin , Mattias Villani

We explore time-varying networks for high-dimensional locally stationary time series, using the large VAR model framework with both the transition and (error) precision matrices evolving smoothly over time. Two types of time-varying graphs…

Methodology · Statistics 2023-02-07 Jia Chen , Degui Li , Yuning Li , Oliver Linton

We consider the problem of approximating sums of high-dimensional stationary time series by Gaussian vectors, using the framework of functional dependence measure. The validity of the Gaussian approximation depends on the sample size $n$,…

Statistics Theory · Mathematics 2015-08-31 Danna Zhang , Wei Biao Wu

In this paper we study covariance estimation with missing data. We consider missing data mechanisms that can be independent of the data, or have a time varying dependency. Additionally, observed variables may have arbitrary (non uniform)…

Statistics Theory · Mathematics 2021-06-17 Eduardo Pavez , Antonio Ortega

The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from…

Statistics Theory · Mathematics 2016-08-16 Nicolai Meinshausen , Peter Bühlmann

CoVariance Neural Networks (VNNs) perform convolutions on the graph determined by the covariance matrix of the data, which enables expressive and stable covariance-based learning. However, covariance matrices are typically dense, fail to…

Machine Learning · Computer Science 2026-01-21 Andrea Cavallo , Samuel Rey , Antonio G. Marques , Elvin Isufi

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…

Statistics Theory · Mathematics 2025-12-16 Bufan Li , Xinghao Qiao , Weichi Wu , Holger Dette

Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…

Methodology · Statistics 2023-08-08 Sagnik Bhadury , Riten Mitra , Jeremy T. Gaskins

Multivariate processes with long-range dependent properties are found in a large number of applications including finance, geophysics and neuroscience. For real data applications, the correlation between time series is crucial. Usual…

Statistics Theory · Mathematics 2015-11-02 Sophie Achard , Irène Gannaz

High-dimensional time series datasets are becoming increasingly common in many areas of biological and social sciences. Some important applications include gene regulatory network reconstruction using time course gene expression data, brain…

Methodology · Statistics 2021-08-02 Sumanta Basu , David S. Matteson