分野別セミナー

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 variable selection consistency, including the case when the regularizer is non-convex. These theoretical results are supported by empirical studies.