This paper presents results on the fractal and statistical behavior of cosmic ray time series detected in an air shower experiment located at 2000-m altitude above the underground Gran Sasso Laboratory, Italy. We consider single particles (muons), corresponding to primary energies of ≥10 GeV, and air showers, corresponding to primary energies of ≥80 TeV. For all time series the analysis indicates a clear stochastic monofractal, non-Gaussian character; comparing these results with those obtained for underground muons and for neutron monitors, we conclude that these properties likely belong in general to cosmic ray time series, irrespective of the nature of the particles and the energies of their progenitors. In particular, the air shower time series from high-energy primaries have a fractal dimension larger than the single-muon time series originating from low-energy primaries. ¿ American Geophysical Union 1993