Much work has been done on trying to gain insight into the dynamics of accreting systems, such as black hole and neutron star binaries, by analyzing timing measurements from X-ray telescopes. In this thesis we present a novel approach to this problem using a kurtosis measure of the wavelet distribution obtained from the light curve to quantify the presence of intermittent activity. This method is applied to large RXTE data sets for GRS 1915+105, and Cygnus X-1. We demonstrate a new approach to reveal bursting modes. Negative correlation between the presence of a low frequency QPO in the Cygnus X-1 Fourier power spectrum and a wavelet kurtosis indicator of temporal intermittency is observed. A possible interpretation of this anti-correlation is developed using a "dripping handrail" transient chaos model.