In this article, we use half hourly spot electricity prices and load data for the National Electricity Market (NEM) of Australia for the period from December 1998 to August 2007 to test for randomly modulated periodicity. In doing so, we apply signal coherence spectral analysis to the time series of half hourly spot prices and megawatt-hours (MWh) load demand from 711211998 to 3110812007 using the FORTRAN 95 program developed by Hinich (2000). We detect relatively steady weekly and daily cycles in load demand but relatively more unstable cycles in prices.