This paper presents the first application of multichannel singular spectrum analysis (M-SSA) to radar satellite geodesy. We apply M-SSA to Sentinel-1 Interferometric Synthetic Aperture Radar (InSAR) time series processed for Pacaya Volcano in Guatemala in two steps. First, we produce, in an iterative and data-adaptive way, estimates of missing data points to obtain evenly sampled time series. The resulting time series are then decomposed with M-SSA into long-periodic nonlinear trends and oscillatory modes providing a sparse representation of the signals present in the data. The M-SSA approach presented herein is designed to deal with very large datasets such as collections of InSAR time series. Combining M-SSA with power spectrum analysis show that the dominant frequencies of the main oscillatory modes correspond to 1, 1.5, 2, 3, 5.8 and 6.8 cycle per years. These frequencies are consistent with the seasonal variability of the regional hydrological system, as determined from correlograms of rainfall time series and M-SSA modes extracted from time series of regional gravity anomalies using Gravity Recovery and Climate Experiment (GRACE) data, Global Navigation Satellite Systems (GNSS) time series recorded in Guatemala City, and phase delay maps derived from a global weather model. While some of the seasonal oscillations correlate well with topography, others show significant spatial asymmetries. The extracted nonlinear trends show large amplitudes around the summit and within the area covered by the 2014 lava flows and, to a lesser extent, the 2010 lava flows. This nonlinear trend correlates with interannual variability of the regional water cycle.