A consistent nonparametric test of ergodicity for time series with applications

We propose a set of algorithms for testing the ergodicity of empirical time series, without reliance on a specific parametric framework. It is shown t hat the resulting test asymptotically obtains the correct size for stationa ry and nonstationary processes, and maximal power against non-ergodic but s tationary alternatives. The test will not reject in the presence of nonstat ionarity that does not lead to ergodic failure. The method is used to inves tigate debates over stability of monetary aggregates relative to GDP, and t he mean reversion hypothesis with respect to high frequency data on exchang e rates. Both the Monte Carlo and data analysis results suggest that the te st has good size and power performance. (C) 2001 Elsevier Science S.A. All rights reserved.