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A consistent nonparametric test of ergodicity for time series with applications

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  • Domowitz, Ian
  • El-Gamal, Mahmoud A.

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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 102 (2001)
Issue (Month): 2 (June)
Pages: 365-398

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Handle: RePEc:eee:econom:v:102:y:2001:i:2:p:365-398

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Web page: http://www.elsevier.com/locate/jeconom

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References

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Cited by:
  1. repec:att:wimass:9719 is not listed on IDEAS
  2. Jakob Grazzini, 2012. "Analysis of the Emergent Properties: Stationarity and Ergodicity," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 15(2), pages 7.
  3. El-Gamal, Mahmoud A. & Ryu, Deockhyun, 2006. "Short-memory and the PPP hypothesis," Journal of Economic Dynamics and Control, Elsevier, vol. 30(3), pages 361-391, March.
  4. Chang, Yoosoon & Sickles, Robin & Song, Wonho, 2001. "Bootstrapping Unit Root Tests with Covariates," Working Papers 2001-07, Rice University, Department of Economics.
  5. Deockhyun Ryu & Mahmoud A. El-Gamal, 2004. "Short Memory and the PPP-puzzle," Econometric Society 2004 Far Eastern Meetings, Econometric Society 577, Econometric Society.
  6. Corradi, Valentina & Swanson, Norman R. & White, Halbert, 2000. "Testing for stationarity-ergodicity and for comovements between nonlinear discrete time Markov processes," Journal of Econometrics, Elsevier, Elsevier, vol. 96(1), pages 39-73, May.
  7. Lopes, Sílvia R.C. & Prass, Taiane S., 2014. "Theoretical results on fractionally integrated exponential generalized autoregressive conditional heteroskedastic processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 278-307.

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