Context. Solar wind disturbances such as interplanetary coronal mass ejections (ICMEs) and corotating interaction regions (CIRs) cause short-term cosmic ray depressions, generally denoted as Forbush decreases. Aims. We conduct a systematic statistical study of various aspects of Forbush decreases. The analysis provides empirical background for physical interpretations of short-term cosmic ray modulations. Methods. Firstly, we analyzed the effects of different types of solar wind disturbances, and secondly, we focused on the phenomenon of over-recovery (the return of the cosmic ray count to a value higher than the pre-decrease level). The analysis is based on groundbased neutron monitor data and the solar wind data recorded by the Advanced Composition Explorer. The correlations between various cosmic ray depressions and solar wind parameters as well as their statistical significance are analyzed in detail. In addition, we performed a normalized superposed epoch analysis for depressions and magnetic field enhancements. Results. The analysis revealed differences in the relationship between different solar wind disturbances and cosmic ray depression parameters. The amplitude of the depression for ICMEs was found to correlate well with the amplitudes of magnetic field strength and fluctuations, whereas for CIRs we found only the correlation between the amplitude of the depression and the solar wind disturbance dimension proxy vt B . Similar behavior was found for shock and no-shock events, respectively. The CIR/ICME composites show a specific behavior that is a mixture of both ICMEs and CIRs. For all analyzed categories we found that the duration of the depression correlates with the duration of the solar wind disturbance. The analysis of the over-recovery showed that there is no straightforward relationship to either "branching-effect" or geomagnetic effects, therefore we propose a scenario where the "branching-effect" is caused by several factors and is only indirectly related to the over-recovery.