Flexible Bayesian Time-Series Models in a Data-Rich Environment

<p dir="ltr">This dissertation contains four essays that contribute to the development of flexible Bayesian time-series models that adapt to nonlinearities, missing data and time-varying volatility in high-dimensional settings, with applications in business cycle analysis, inflation forecasting, empirical asset pricing, and Bayesian model comparison. Chapter 1 outlines the broader theme of our research, which focuses on two important domains of Bayesian econometrics: Bayesian dynamic factor models and large Bayesian vector autoregressions (VARs). </p><p dir="ltr">As part of the first topic, in Chapter 2, we develop Asymmetric Dynamic Factor Models that allow the factor loadings to vary depending on whether the factors exceed a threshold. In Chapter 3, we propose Matrix Dynamic Factor Models (MDFM) to preserve the matrix structure commonly observed in macroeconomic and financial economic panels, aiming to provide more interpretable factors and loadings while also to reduce the computational cost. Chapter 4 builds on the MDFMs to address the missing data problems and provides a granular approach to forecasting inflation and constructing price risk indicators for the euro area.</p><p dir="ltr">The second part of our research, in Chapter 5, focuses on scalable Bayesian model comparison for large VARs. In response to the increasing use of stochastic volatility specifications following the COVID-19 pandemic, we propose a variational importance sampling estimator of marginal likelihood that combines variational Bayes and importance sampling method. Our method substantially reduces the computational burden in both estimation and the model comparison, as it does not rely on the Markov chain Monte Carlo methods.</p>