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

Non-Asymptotic Properties of Regularized Multivariate ARCH models

Benjamin Poignard (Osaka University)

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4. Non-Asymptotic Properties of Regularized Multivariate ARCH models

大阪大学 数理・データ科学セミナー データ科学セミナーシリーズ 第32回

Non-Asymptotic Properties of Regularized Multivariate ARCH models

Benjamin Poignard (Osaka University)

We provide finite sample properties of regularized multivariate ARCH processes, where the linear representation of ARCH models allows for an ordinary least square estimation. Under the restricted strong convexity of the unpenalized loss function, regularity conditions on the regularizer, strict stationary and beta-mixing process, we prove non-asymptotic error bounds on the regularized ARCH estimators. Moreover, based on the primal-dual witness method, we establish variables selection consistency, including the case when the regularizer is non-convex. These theoretical results are supported by simulation studies.