Kolmogorov–Smirnov, Fluctuation, and Z_<i>g</i>Tests for Convergence of Markov Chain Monte Carlo Draws

Abstract

We examine the sizes and powers of three tests of convergence of Markov Chain Monte Carlo draws: the Kolmogorov–Smirnov test, fluctuation test, and Geweke's test. We show that the sizes and powers are sensitive to the existence of autocorrelation in the draws. We propose a filtered test that is corrected for autocorrelation. We present a numerical illustration using the Federal funds rate.