Abstract The astrophysical stochastic gravitational wave background (SGWB) is mostly produced from unresolved stellar binary mergers, and the number of events at any moment of time is expected to be Poisson-distributed. The event rate is governed by several astrophysical processes. The Poisson nature leads to variation in the number of sources and this causes temporal variations in the SGWB. The intrinsic temporal fluctuations of the SGWB are a rich source of astrophysical information that can be explored via ongoing and future gravitational wave experiments to classify the sources of the SGWB signal. Along with several other methods to estimate the GW event rates from individual sources, the study of the temporal variations of the SGWB signal provides an independent method for estimating the event rates of the GW sources that contribute to the SGWB. Along with direct estimates of event rates, this approach can also distinguish between different sources contributing to the SGWB signal and will be a useful probe of its evolution over a vast cosmic volume. On averaging over observation times, the SGWB will be statistically invariant under time translation. Statistical time translation symmetry of the SGWB is expected due to the negligible evolution of the relevant cosmological and astrophysical phenomena over the observation time-scales over which the data is collected.