One of three criteria to demonstrate self-organized criticality (SOC) for a critical phenomenon is that time arrival of events displays a frequency dependence which is inversely proportional to frequency (f) to some power. That is, for SOC, the power spectrum in the frequency (f) domain is supposed to fall off as 1/f¿, where ¿ is typically a number between 1 and 2. Avalanche phenomena have been used as prototypes for illustrating SOC, and therefore it is of interest as to whether snow avalanches follow the criterion. In this paper, time series analyses of mass arrivals from 20 years of records constituting ~10,000 avalanches are presented for Bear Pass and Kootenay Pass, British Columbia. The results suggest that the autocorrelation functions and partial autocorrelation functions of the series fall off in an exponential manner so that the implied power spectra in the frequency domain, given by the Fourier transforms of the autocorrelation functions, decay with frequency in a manner which is not strictly consistent with SOC. In common with SOC, the power spectra are suggested to have most content in the low-frequency events and the spectra do not constitute white noise. However, given the limitations on the data sampling and recording, it cannot be definitively stated that the power spectra fall off with 1/f¿ as required for SOC.