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 that the resulting test asymptotically obtains the correct size for stationary and nonstationary processes, and maximal power against non-ergodic but stationary alternatives. The test will not reject in the presence of nonstationarity that does not lead to ergodic failure. The method is used to investigate debates over stability of monetary aggregates relative to GDP, and the mean reversion hypothesis with respect to high frequency data on exchange rates. Both the Monte Carlo and data analysis results suggest that the test has good size and power performance.