Modeling and Estimation of High-dimensional Vector Autoregressions.

[摘要] Vector Autoregression (VAR) represents a popular class of time series models in applied macroeconomics and finance, widely used for structural analysis and simultaneous forecasting of a number of temporally observed variables. Over the years it has gained popularity in the fields of control theory, statistics, economics, finance, genetics and neuroscience.In addition to the ;;curse of dimensionality;; introduced by a quadratically growing dimension of the parameter space, VAR estimation poses considerable challenges due to the temporal and cross-sectional dependence in the data. In the first part of this thesis, we discuss modeling and estimation of high-dimensional VAR from short panels of time series, with applications to reconstruction of gene regulatory network from time course gene expression data. We investigate adaptively thresholded lasso regularized estimation of VAR models and propose a thesholded group lasso regularization framework to incorporate a priori available pathway information in the model. The properties of the proposed methods are assessed both theoretically and via numerical experiments. The study is illustrated on two motivating examples coming from functional genomics and financial econometrics.The second part of this thesis focuses on modeling and estimation of high-dimensional VAR in the traditional time series setting, where one observes asingle replicate of a long, stationary time series. We investigate the theoretical properties of l1-regularized and thresholded estimators in high-dimensional VAR, stochastic regression and covariance estimation problems in a non-asymptotic framework. We establish consistency of the estimators under high-dimensional scaling and propose a measure of stability that provides insight into the effect of temporal and cross-sectional dependence on the accuracy of the regularized estimates. We also propose alow-rank plus sparse modeling strategy of high-dimensional VAR in the presence of latent variables. We study the theoretical properties of the proposed estimator in a non-asymptotic framework, establish its estimation consistency under high-dimensional scaling and compare its performance with existing methods via extensive simulation studies.

[发布机构] University of Michigan

[效力级别] Time Series

[关键词] High-dimensional Statistics;Time Series;Vector Autoregression;Granger Causality;Statistics and Numeric Data;Science;Statistics