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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 ℝd 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.

Suggested Citation

  • Domowitz, Ian & El-Gamal, Mahmoud A., 1993. "A Consistent Test of Stationary-Ergodicity," Econometric Theory, Cambridge University Press, vol. 9(4), pages 589-601, August.
    • Handle: RePEc:cup:etheor:v:9:y:1993:i:04:p:589-601_00
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    Cited by:

    1. 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.
    2. Christiano, Lawrence J. & G. Harrison, Sharon, 1999. "Chaos, sunspots and automatic stabilizers," Journal of Monetary Economics, Elsevier, vol. 44(1), pages 3-31, August.
    3. 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, vol. 96(1), pages 39-73, May.
    4. 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.
    5. Deockhyun Ryu & Mahmoud A. El-Gamal, 2004. "Short Memory and the PPP-puzzle," Econometric Society 2004 Far Eastern Meetings 577, Econometric Society.
    6. 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.
    7. 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.
    8. 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.
    9. Guilmi, Corrado Di & Fujiwara, Yoshi, 2022. "Dual labor market, financial fragility, and deflation in an agent-based model of the Japanese macroeconomy," Journal of Economic Behavior & Organization, Elsevier, vol. 196(C), pages 346-371.
    10. Domowitz, I. El-Gamal, M., 1997. "Financial Market Structure and the Ergocicity of Prices," Working papers 9719, Wisconsin Madison - Social Systems.
    11. Albert Marcet & Guido Lorenzoni, 1998. "Parameterized expectations approach; Some practical issues," Economics Working Papers 296, Department of Economics and Business, Universitat Pompeu Fabra.

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