Partial group delay is a spectral parameter, which measures the time lag between two time series in a system after the spurious effects of the other series in the system have been eliminated. For weakly-stationary processes, estimators for partial group delay are proposed based on indirect and direct approaches. Conditions for weak consistency and asymptotic normality of the proposed estimators are obtained. Applications to a multiple test of partial group delay are investigated. The time lag interpretation of partial group delay is justified, which provides insight into the nature of linear relationships among weakly-stationary processes. Extensions are made to group delay estimation and partial group delay estimation for non-stationary "oscillatory" processes. / Ph. D.