This thesis focuses on two statistical challenges in time-series modelling. The first is when variables’ observations are available at different frequencies. The second is when the coefficients of a model are time-varying with stochastic volatility. The impact of these challenges and the value of the suggested remedies are assessed in empirical financial-economic applications.

In addressing the first statistical challenge, disaggregation from the low- to the highfrequency domain is one of the methods that has long been used in several pieces of literature. The first chapter evaluates the existing disaggregation methods with thorough comparisons to provide comprehensive guidance for an empirical user. The second chapter builds on these results to examine the value-added in forecasting the volatility of financial stock prices by incorporating information from variables with mixed frequencies such as market sentiment indicators, economic variables, and activity measures. A representative factor(s) of all potential predictors from both frequencies results in significant forecast gains in predicting long-term financial volatility even during the 2007-08 financial crisis.

The third chapter proposes a state-space model to incorporate features of timevarying coefficients to reflect the dynamic relationship between the dependent and the explanatory variables. Mainly, the model consists of two hierarchical states. First, the time-varying coefficients follow an autoregressive (AR) process with heteroskedastic innovations. Second, the log-transformation of the conditional variance of these innovations is also modelled as an AR process. In an empirical study, we utilize the proposed methodology to forecast the volatility of financial stock prices. We find that the proposed features consistently and significantly enhance the forecasting accuracy compared to a benchmark model and its existing variants.