This thesis develops computationally efficient statistical methodologies for large-scale time series with complex dependence structures. As modern sensing technologies generate increasingly large datasets, classical likelihood-based inference often becomes computationally prohibitive, motivating the need for scalable alternatives. The first contribution extends the Generalized Method of Wavelet Moments (GMWM) to account for vibration-induced noise in inertial sensor calibration, improving navigation accuracy. The second introduces the Generalized Method of Wavelet Moments with eXogenous inputs (GMWMX), a computationally efficient estimator for regression models with correlated errors, enabling scalable inference for large collections of time series. The third develops the Wavelet Moment Regression Estimator (WAMORE), extending this framework to regression models with missing observations while establishing its theoretical properties and introducing a computationally efficient model selection criterion. The proposed methodologies are illustrated through applications in inertial navigation and large Global Navigation Satellite System (GNSS) networks for estimating tectonic velocities and crustal deformation.