A new method is presented for statistical analysis of long-term time series of water level observations aimed at distinguishing short-term disturbances; observation data from the YuZ-5 well, located in the Petropavlovsk Geodynamic Test Area, eastern Kamchatka, are considered. These data (from July 27, 2012, to February 1, 2018) are remarkable for their degree of detail: the sampling rate of the water level and atmospheric pressure measurements was 5 min and the sensitivity (accuracy) was ±0.1 cm for water level recording and ±0.1 hPa for atmospheric pressure. Also, five strong earthquakes with Mw = 6.5–8.3 occurred at epicentral distances of de = 80–700 km during the observation period. A thorough analysis of the hydrodynamic regime of the observation well over a long period and the high quality of observation data, together with the data on strong seismic events, allow us to consider the possibility of using formalized statistical methods of water level data processing for diagnostics of anomalous conditions. As a result of factor and cluster analysis applied to the sequence of multidimensional vectors of the statistical properties of water level time series in successive one-day-long time windows, after adaptive compensation for atmospheric pressure, four different statistically significant states of time series, replacing each other in time, are distinguished. Geophysical interpretation of the anomalous conditions of the water level time series (with a probability of 0.013) is carried out in comparison to strong earthquakes, technical conditions of observations, and seasonal features of the hydrodynamic regime in the observation well. It is shown that this method of water level data processing can detect short-term anomalies in the hydrogeodynamic regime of a well, significantly supplementing traditional processing of water level data aimed mostly at finding low-frequency trends in water level changes. This method can be applied in geophysical monitoring and prediction of earthquakes from online processing of water level data in wells.