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A model for level induced conditional heteroskedasticity

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  • Michel, Jon
  • de Jong, Robert M.

Abstract

A class of conditional heteroskedasticity models is introduced and analyzed. This class of models is motivated by the desire to allow the level of a GARCH process to influence the volatility. We show the existence of a unique strictly stationary solution which is β-mixing. The analysis of this model does not rely upon Markov chain methods.

Suggested Citation

  • Michel, Jon & de Jong, Robert M., 2019. "A model for level induced conditional heteroskedasticity," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 293-300.
    • Handle: RePEc:eee:stapro:v:145:y:2019:i:c:p:293-300
    DOI: 10.1016/j.spl.2018.10.011
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    References listed on IDEAS

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    1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    2. David G. Hobson & L. C. G. Rogers, 1998. "Complete Models with Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 27-48, January.
    3. 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.
    4. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    5. Michel, Jon & de Jong, Robert M., 2018. "Mixing properties of the dynamic Tobit model with mixing errors," Economics Letters, Elsevier, vol. 162(C), pages 112-115.
    6. Enrique Sentana, 1995. "Quadratic ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(4), pages 639-661.
    7. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
    8. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(3), pages 458-467, December.
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