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Essays in High-dimensional Econometrics and Finance
Pyrlik, Vladimir ; Anatolev, Stanislav (advisor) ; Volkov, Vladimir (referee) ; Prokhorov, Artem (referee)
Essay in High-Dimensional Econometrics and Finance Vladimir Pyrlik Abstract High dimensionality is a popular contemporary setting in applied statistical analysis of various types of data. Growing dimensionality of the data challenges precise and well-conditioned estimates of statistical models. We address selected high-dimensional methods and their applications to financial market analysis. First, we consider modeling flexible joint distributions using copulas. In Chapter 1, we address estimation of Gaussian and t copulas in ultra-high dimensions, up to thousands of variables that use up to 30 times shorter sample lengths. We employ large covariance matrix shrinkage tools to obtain precise and well-conditioned estimates of the matrix parameters of the copulas. In Chapter 2, we present a new method for estimating the skew-t copula, known for its advantageous properties in characterizing joint distributions, including asymmetry, heavy tails, and asymmetric tail dependence. Our approach involves a two-step procedure based on the simulated method of moments and analytical non-linear shrinkage estimator for large covariance matrices. In both chapters, we also illustrate the benefits of the copula approach in a large stock portfolio allocation. Our analysis shows that copula-based models deliver better portfolios...
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