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

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

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-o...

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Bibliographic Details
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
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10224232