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A Consistent Test of Stationary Ergodicity

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

Abstract

A formal statistical test of stationary-ergodicity is developed for known Markovian processes on null null This makes it applicable to testing models and algorithms, as well as estimated time series processes ignoring the estimation error. The analysis is conducted by examining the asymptotic properties of the Markov operator on density space generated by the transition in the state space. The test is developed under the null of stationary-ergodicity, and it is shown to be consistent against the alternative of nonstationary-ergodicity. The test can be easily performed using any of a number of standard statistical and mathematical computer packages.
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Suggested Citation

  • Domowitz, Ian & El-Gamal, Mahmoud A., 1993. "A Consistent Test of Stationary Ergodicity," Working Papers 794, California Institute of Technology, Division of the Humanities and Social Sciences.
  • Handle: RePEc:clt:sswopa:794
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. 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, pages 39-73.
    2. Domowitz, Ian & El-Gamal, Mahmoud A., 2001. "A consistent nonparametric test of ergodicity for time series with applications," Journal of Econometrics, Elsevier, vol. 102(2), pages 365-398, June.
    3. Kim, Hyeongwoo & Ryu, Deockhyun, 2015. "Measuring the speed of convergence of stock prices: A nonparametric and nonlinear approach," Economic Modelling, Elsevier, vol. 51(C), pages 227-241.
    4. Christiano, Lawrence J. & G. Harrison, Sharon, 1999. "Chaos, sunspots and automatic stabilizers," Journal of Monetary Economics, Elsevier, vol. 44(1), pages 3-31, August.
    5. 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.
    6. Domowitz, I. El-Gamal, M., 1997. "Financial Market Structure and the Ergocicity of Prices," Working papers 9719, Wisconsin Madison - Social Systems.
    7. Grazzini, Jakob & Richiardi, Matteo, 2015. "Estimation of ergodic agent-based models by simulated minimum distance," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 148-165.
    8. Albert Marcet & Guido Lorenzoni, 1998. "Parameterized expectations approach; Some practical issues," Economics Working Papers 296, Department of Economics and Business, Universitat Pompeu Fabra.
    9. Deockhyun Ryu & Mahmoud A. El-Gamal, 2004. "Short Memory and the PPP-puzzle," Econometric Society 2004 Far Eastern Meetings 577, Econometric Society.
    10. 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 1-7.

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