A Consistent Nonparametric Test of Ergodicity for Time Series with Applications

46 Pages Posted: 18 Oct 1999

See all articles by Ian Domowitz

Ian Domowitz

ITG, Inc.; National Bureau of Economic Research (NBER)

Mahmoud El-Gamal

Rice University - Department of Economics

Date Written: March 1999


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.

JEL Classification: C1, C4, G0

Suggested Citation

Domowitz, Ian H. and El-Gamal, Mahmoud A., A Consistent Nonparametric Test of Ergodicity for Time Series with Applications (March 1999). Available at SSRN: https://ssrn.com/abstract=179912 or http://dx.doi.org/10.2139/ssrn.179912

Ian H. Domowitz (Contact Author)

ITG, Inc. ( email )

380 Madison Avenue, 4th Floor
Electronic Market Initiatives
New York, NY 10017
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Mahmoud A. El-Gamal

Rice University - Department of Economics ( email )

6100 South Main Street
Houston, TX 77005
United States
713-737-6301 (Phone)
713-737-5879 (Fax)

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