Estimation and Inference of Large Dimensional Unobservable Dynamic Uncertainties

Description

In recent years, there has been a broad rejection of static regression models in favor of capturing unobservable time-varying uncertainties. Meanwhile, both increasingly available empirical observations and economic theory, such as the Arbitrage Pricing Theory (APT), encourage close investigation of large panel data, where there are many individuals in a certain sampling period. When estimating regression models, constructing density function, managing risks and allocating portfolios, econometric models that could enable accurate estimation of their large dimensional dynamic uncertainties would help avoid potential loss of information, estimation bias and misspecification errors that can stem from static regression models with a small number of cross-sectional entities. Because of its parsimonious approximation of time-varying behavior of unobservable uncertainties, Bollerslev, Engle, and Wooldridge’s (1988) multivariate generalized autoregressive heteroscedastic (GARCH) process has become perhaps the most common approach used to capture dynamic volatilities; however, due to curse of dimensionality, it has long been limited to a finite panel setting, even incapable capturing the dynamic co-movement for moderate panel data for decades such as 25 aggregate portfolios sorted by size and book-to-market ratios. I am proposing the development of a novel machine learning estimation methodology for the general class of high dimensional multivariate GARCH models; this methodology can preserve a channel for lagged values and past innovations to affect dynamic volatility. This project will contribute to the financial econometrics and machine learning literature by establishing the large sample properties of the proposed large dimensional dynamic uncertainty estimator, which is guaranteed to be positive definite in finite samples with a fast rate of convergence. To ease its implementation, my proposed project will further develop an efficient algorithm and derive a generalized cross-validation criterion to optimally select the tuning parameter in practice. This project can also significantly aid practical financial analysis given the presence of increasingly available high-dimensional financial data. We will further apply the proposed estimation method to financial practices, such as vast portfolio selections or capturing dynamic risk premiums in the presence of latent time-varying factors. I expect that my project could provide additional insight and significantly benefit financial and economic studies in the big data era.