<p dir="ltr">This dissertation develops new methods for handling uncertainty and persistence in time series analysis. It introduces a consistent OLS-based approach for dating financial bubbles, a forecast combination method that improves accuracy in near-unit root environments using accumulated prediction errors, and a Mallows-weighted strategy for forecasting cointegrated systems by balancing long- and short-run dynamics. Simulation studies and empirical applications confirm the effectiveness of these approaches across various economic contexts.</p>