Year: 2018
Type: preprint
Abstract: We provide finite sample properties of sparse multivariate ARCH processes, where the linear representation of ARCH models allows for an ordinary least squares estimation. Under the restricted strong convexity of the unpenalized loss function, regularity conditions on the penalty function, strict stationary and beta-mixing process, we prove non-asymptotic error bounds on the regularized ARCH estimator. Based on the primal-dual witness method of Loh and Wainwright (2017), we establish variable selection consistency, including the case when the penalty function is non-convex. These theoretical results are supported by empirical studies.
Source: arXiv (Cornell University)
Author: Poignard, Benjamin
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2886659109