Forecasting high-dimensional, time-varying variance-covariance matrices with high-frequency data and sampling Pólya-Gamma random variates for posterior distributions derived from logistic likelihoods
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The first portion of this thesis develops efficient samplers for the Pólya-Gamma distribution, an essential component of the eponymous data augmentation technique that can be used to simulate posterior distributions derived from logistic likelihoods. Building fast computational schemes for such models is important due to their broad use across a range of disciplines, including economics, political science, epidemiology, ecology, psychology, and neuroscience. The second portion of this thesis explores models of time-varying covariance matrices for financial time series. Covariance matrices describe the dynamics of risk and the ability to forecast future variance and covariance has a direct impact on the investment decisions made by individuals, banks, funds, and governments. Two options are pursued. The first incorporates information from high-frequency statistics into factor stochastic volatility models while the second models high-frequency statistics directly. The performance of each is assessed based upon its ability to hedge risk within a class of similarly risky assets.