Augmented Graphical Ridge Estimation with Application in the Cryptocurrency Market

Abstract Cryptocurrency markets exhibit complex and evolving structures, making it challenging to identify appropriate models that can effectively capture their returns, particularly in high-dimensional settings. This paper presents a two-step augmented graphical ridge estimator for precision matrix estimation in Gaussian graphical models. The proposed estimator combines $$L_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> and Frobenius norm penalties to improve estimation accuracy compared to existing methods. Simulation studies demonstrate its superior performance under various conditions. When applied to thirty cryptocurrencies from 2019 to 2021, the estimator reveals the dynamic interconnections within the market, offering valuable insights into the structure of the cryptocurrency network and dependencies across assets.