The results of the analysis of continuous, precise time series of observations of the atmospheric pressure and groundwater level in a well drilled to a depth of 400 m and located in the territory of Moscow are presented. These observations are remarkable in terms of their duration which is more than 22 years (from February 2, 1993 to April 4, 2015) and by the sampling interval which is 10 min. Such a long duration of the observations allows exploring the question of how stationary the properties of hydrogeological time series are in a seismically quiet region, which is important from the methodological standpoint for the interpretation of similar observations conducted in seismically active regions for the purposes of earthquake prediction. As a result of applying the factor and cluster analysis to the sequence of multivariate vectors of the statistical properties of the time series of groundwater level observations in successive time windows with a length of 10 days, after the adaptive compensation for the atmospheric pressure effects, five different statistically significant states of the time series between which the transitions take place are distinguished. An attempt of geophysical interpretation of the revealed states is made. The spectral analysis of the sequence of times of the transitions between the clusters identified two significant periods 46 and 275 days.