AUTHOR=Vieira Leonardo Ieracitano , Laurini Márcio Poletti 

TITLE=Multivariate realized volatility: an analysis via shrinkage methods for Brazilian market data

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=Volume 10 - 2024

YEAR=2024

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2024.1379891

DOI=10.3389/fams.2024.1379891

ISSN=2297-4687

ABSTRACT=This work analyzes the realized volatility of assets in the Brazilian market within a multivariate framework.While volatility models have demonstrated notable performance in the univariate context, challenges arise with the escalating dimensionality of the covariance matrix and the lower asset liquidity in emerging markets. Utilizing intraday stock trading data from Brazilian Market, we compute daily covariance matrices employing diverse specifications. To address the issue of dimensionality in the estimation of covariance matrices, we employ penalization restrictions on the coefficients through regressions with shrinkage. We use Ridge, LASSO, or Elastic Net estimators to capture the dynamics of these matrices.The covariance construction models are compared using the Model Confidence Set (MCS) algorithm, which selects the best models based on their predictive performance. The results obtained indicate that the method of estimating the covariance matrix significantly influences the selection of the best models. Furthermore, it is observed that more liquid sectors exhibit greater intra-sectoral dynamics. The results benefit from shrinkage, but the high correlation between assets poses challenges in capturing stock or sector idiosyncrasies.