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Geometric ergodicity and [beta]-mixing property for a multivariate CARR model

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  • Lee, O.
  • Shin, D.W.

Abstract

Multivariate conditional autoregressive range process is considered and conditions for existence of the first moment, stationarity, geometric ergodicity and [beta]-mixing property with exponential decay are obtained.

Suggested Citation

  • Lee, O. & Shin, D.W., 2008. "Geometric ergodicity and [beta]-mixing property for a multivariate CARR model," Economics Letters, Elsevier, vol. 100(1), pages 111-114, July.
    • Handle: RePEc:eee:ecolet:v:100:y:2008:i:1:p:111-114
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    References listed on IDEAS

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    1. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January.
    2. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    3. Tweedie, R. L., 2001. "Drift conditions and invariant measures for Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 92(2), pages 345-354, April.
    4. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Chou, Ray Yeutien, 2005. "Forecasting Financial Volatilities with Extreme Values: The Conditional Autoregressive Range (CARR) Model," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(3), pages 561-582, June.
    7. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(1), pages 17-39, February.
    8. Oswaldo Costa & François Dufour, 2005. "Sufficient condition for the existence of an invariant probability measure for Markov processes," Post-Print hal-00404947, HAL.
    9. Fernandes, Marcelo & de Sa Mota, Bernardo & Rocha, Guilherme, 2005. "A multivariate conditional autoregressive range model," Economics Letters, Elsevier, vol. 86(3), pages 435-440, March.
    10. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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