Student t-tests and compound tests to detect transients in simulated time series

Given a stationary stochastic process, with unknown mean μ, interest often lies in developing estimates and confidence intervals for μ. Unfortunately, if the process is actually only asymptotically stationary, the transient behavior can affect the validity of these estimates and confidence intervals. We present a test for detecting transients in simulation output based on the familiar Student t-test. We also demonstrate and exploit the independence of this t-test and certain other initialization bias tests to construct ‘compound’ initialization bias tests. We demonstrate and evaluate our tests using Monte Carlo simulation.