Mai Phan

• Prices of financial assets fluctuate continuously due to many factors, including economic indicators, geopolitical events, market sentiment and changes in supply and demand. Time series analysis helps to identify underlying patterns and trends in financial data, enabling analysts to make informed predictions about future price movements. Several characteristics of financial time series make this analysis particularly challenging: volatility, non-stationarity, heteroskedasticity, non-normality, and volatility clustering. To address these challenges, advanced time series models such as regime-switching GARCH models have been developed. These models allow for the identification of different regimes within financial time series, where each regime is characterized by a distinct volatility structure and can adapt to periods of high and low volatility. As a result, they capture the dynamic behavior of financial markets more effectively than traditional time series models. This flexibility makes regime-switching GARCH models suitable for analyzing highly volatile financial time series such as cryptocurrencies. Despite their advantages, Markov-Switching GARCH models do not capture abrupt price movements commonly referred to as jumps. This dissertation therefore investigates the modeling and forecasting of cryptocurrency returns by extending classical time series models to incorporate both regime-dependent dynamics and jump components. Several model specifications are developed including models with one jump process and models with two jump processes that distinguish between upward and downward jumps. Corresponding filter equations and parameter estimation methods are derived and the performance of the proposed models is evaluated through a simulation study. The analysis enables a systematic assessment of parameter estimation, regime changes, convergence behavior and out-of-sample forecasting performance based on predicted conditional expectations and conditional variances. The proposed models are compared with benchmark models including ARMA(1,1)-GARCH(1,1) models and Markov-switching GARCH models without jump components. The results indicate that incorporating jump components improves the modeling of cryptocurrency returns and volatility, enhances forecasting accuracy, and contributes to a better understanding of the complex dynamics underlying financial time series.