Initial transient detection in simulations using the second-order cumulant spectrum

Procedures for detecting an initial transient in simulation output data are developed. The tests use the second-order cumulant spectrum which differs from the power spectrum in that the stationarity constraint is not required for the former. The second-order cumulant spectrum can be interpreted as the nonstationary power spectrum and is an orthogonal decomposition of the variance of a nonstationary process. The null hypothesis is that the simulation output data series is a covariance stationary process. Equivalently, all estimates of the second-order cumulant spectrum in the region which excludes the estimates of the power spectrum will have an expected value of zero. The test procedures are designed to detect initialization bias in the estimation of the mean and the variance. These procedures can be extended to detect bias in the moments of cumulants of order n, where n>2. Results are presented from the application of the test to simulated processes with superimposed mean and variance transients and an M/M/1 queue example.