大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

Estimation of High Dimensional Vector Autoregression via Sparse Precision Matrix

Benjamin Poignard (Graduate School of Economics, Osaka University)

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4. Estimation of High Dimensional Vector Autoregression via Sparse Precision Matrix

大阪大学 数理・データ科学セミナー 金融・保険セミナーシリーズ 第122回

Estimation of High Dimensional Vector Autoregression via Sparse Precision Matrix

Benjamin Poignard (Graduate School of Economics, Osaka University)

We consider the problem of estimating sparse structural vector autoregression (SVAR) processes via penalized precision matrix. Such matrix is the output of the underlying directed acyclic graph of the SVAR process, whose zero components correspond to zero SVAR coefficients. The precision matrix estimators are deduced from the class of Bregman divergences and regularized by the SCAD, MCP and LASSO penalties. Under suitable regularity conditions, we derive error bounds for the regularized precision matrix for each Bregman divergence. Moreover, we establish the support recovery property, including the case when the penalty is non-convex. These theoretical results are supported by empirical studies.