High-Dimensional Precision Matrix Estimation through GSOS with Application in the Foreign Exchange Market

• Published in: Mathematics (Basel) Vol. 10; no. 22; p. 4232
• Main Authors: Kheyri, Azam, Bekker, Andriette, Arashi, Mohammad
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-11-2022
• Subjects: Algorithms; Analysis; Currencies; Estimation theory; exchange rate; Fines & penalties; Foreign exchange market; Foreign exchange markets; Gaussian graphical model; graphical elastic net; high-penalized log-likelihood; Matrices; Normal distribution; Operators (mathematics); precision matrix estimation; ridge estimation; Sparsity; South Africa
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math10224232

This article studies the estimation of the precision matrix of a high-dimensional Gaussian network. We investigate the graphical selector operator with shrinkage, GSOS for short, to maximize a penalized likelihood function where the elastic net-type penalty is considered as a combination of a norm-one penalty and a targeted Frobenius norm penalty. Numerical illustrations demonstrate that our proposed methodology is a competitive candidate for high-dimensional precision matrix estimation compared to some existing alternatives. We demonstrate the relevance and efficiency of GSOS using a foreign exchange markets dataset and estimate dependency networks for 32 different currencies from 2018 to 2021.