Stochastic covariances are critical for macroeconomic and financial modelling, particularly in capturing uncertainty and dynamic interdependencies. This study introduces the Dynamic Factor Augmented VAR with Higher-order Multivariate Stochastic Volatility (DFAVAR-HMSV) framework, along with a computationally efficient estimation methodology. The proposed model captures complex dynamic interdependencies, leverage effects, and higher-order persistence in volatility structures. Applying this framework to construct uncertainty indices for Canada and Québec, the study provides critical insights into regional and national macroeconomic dynamics.