The temporal statistics of multiple scattered broadband terahertz pulses through a highly scattering medium is analyzed. The probability distribution function of the scattered field varies with the delay time. The probability distributions of the scattered field, and the real and imaginary components are discussed. Due to the broad bandwidth and the transient nature of the terahertz pulses, the statistics of the scattered field evolves over time and is therefore nonstationary. This analysis emphasizes that these measured fields are not stationary. We demonstrate that the nonstationary process is a direct consequence of the time dependence of the averaged intensity.