Bayesian analysis of time-varying volatility models

This thesis focuses on modeling the volatility of financial time series. The theoretical part introduces various data transformations, selecting logarithmic returns as the most suitable form for volatility analysis. Subsequently, models of conditional heteroskedasticity are presented—specifically ARCH, GARCH, and stochastic volatility (SV) models — both from theoretical and practical perspectives. An introduction to the Bayesian approach follows, which is employed for estimating the aforementioned models using simulation-based techniques, particularly methods for generating samples from posterior distributions. The section concludes with an overview of simulation approaches for posterior sampling and the integration of these models within the Bayesian framework through a review of relevant literature. The empirical part analyzes two financial time series exhibiting signs of heteroskedasticity and volatility clustering. The first series is modeled using ARCH, GARCH, and SV models, with results indicating that the SV model more accurately captures the volatility structure and better adapts to sudden changes. Based on these findings, the second time series is modeled exclusively using the SV model. While posterior parameter distributions are similar across both series, the latent volatility differs, suggesting a distinct risk structure. The thesis also provides general-purpose scripts for estimating the discussed models using the Stan platform.