A Consistent Nonparametric Test of Ergodicity for Time Series with Applications

TLDR: In this article, a set of algorithms for testing the ergodicity of empirical time series, without reliance on a specific parametric framework, is proposed, and the resulting test asymptotically obtains the correct size for stationary and non-stationary processes, and maximal power against non-ergodic but stationary alternatives.

Abstract: 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 work is linked to recent research on reformulations of the concept of integrated processes of order zero, and we demonstrate the means to operationalize new concepts of "short memory" for economic time series. Limited Monte Carlo evidence is provided with respect to power against the non-stationary and non-ergodic alternative of unit root processes. 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. The test also is applied to other macroeconomic time series, as well as to very high frequency data on asset prices. Both the Monte Carlo and data analysis results suggest that the test has very promising size and power.