Robust estimation of high-dimensional volatility models with and without regime changes

• Grant number: 24/21327-2
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: February 01, 2025
• End date: January 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Applied Probability and Statistics
• Principal Investigator: Luiz Koodi Hotta
• Grantee: Tiago Francisco Pinheiro Gomes
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 23/02538-0 - Time series, wavelets, high dimensional data and applications, AP.TEM

Abstract

Volatility estimation is important in finance, for example, in asset pricing, risk management, and portfolio selection. Given this importance, several multivariate models have emerged. However, various studies consider that most models, or the way their estimates were initially proposed, are not suitable for high-dimensional settings. The main issue lies in the need to estimate a large number of parameters while ensuring that the estimated matrix remains positive definite. Some of the existing approaches are factor models. Another approach is to seek estimation methods for multivariate models that are feasible for high dimensions. In this case, one alternative that will be considered in the project is the use of composite likelihood and the shrinkage method applied to covariance matrix estimates. At the same time, a stylized fact in finance is the presence of outliers and structural breaks. Both factor-based methods and likelihood-based estimates, as well as models that do not allow for more than one regime, are inadequate. Regime-switching models are only feasible in low-dimensional settings. Therefore, when applied directly to the series, low dimensions will be considered. In the case of high-dimensional data, regime-switching models will be applied to the factors. The aim of the project is to study methods and models that are suitable primarily for high-dimensional cases, while also being robust to outliers and allowing for multiple regimes. Robustness can be considered at different levels. At the first level, it involves the estimation of model parameters and conditional covariances. At the second level, it concerns the implications for applications. For example, if we are selecting a minimum variance portfolio, it is crucial to understand the effect of outliers on the variance of the selected portfolio and how we can robustify the method to minimize these impacts.