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V-uniform ergodicity of a continuous time asymmetric power GARCH(1,1) model

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  • Lee, Oesook

Abstract

A continuous time asymmetric power GARCH(1,1) model is presented and the V-uniform ergodicity and β-mixing property of the process with exponential decay rate are proved. The V-uniform ergodicity of the COGARCH(1,1) model is obtained as a special case.

Suggested Citation

  • Lee, Oesook, 2012. "V-uniform ergodicity of a continuous time asymmetric power GARCH(1,1) model," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 812-817.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:4:p:812-817
    DOI: 10.1016/j.spl.2012.01.006
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    References listed on IDEAS

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    1. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    2. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    3. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    4. Ross A. Maller & Gernot Muller & Alex Szimayer, 2008. "GARCH modelling in continuous time for irregularly spaced time series data," Papers 0805.2096, arXiv.org.
    5. Hentschel, Ludger, 1995. "All in the family Nesting symmetric and asymmetric GARCH models," Journal of Financial Economics, Elsevier, vol. 39(1), pages 71-104, September.
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. P. Brockwell, 2001. "Lévy-Driven Carma Processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(1), pages 113-124, March.
    8. S. Haug & C. Klüppelberg & A. Lindner & M. Zapp, 2007. "Method of moment estimation in the COGARCH(1,1) model," Econometrics Journal, Royal Economic Society, vol. 10(2), pages 320-341, July.
    9. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    10. Kallsen, Jan & Vesenmayer, Bernhard, 2009. "COGARCH as a continuous-time limit of GARCH(1,1)," Stochastic Processes and their Applications, Elsevier, vol. 119(1), pages 74-98, January.
    11. 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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