Modeling and Estimation of High-dimensional Vector Autoregressions
نویسندگان
چکیده
Modeling and Estimation of High-dimensional Vector Autoregressions by Sumanta Basu Chair: George Michailidis 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 highdimensional 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
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