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Parametric inference and forecasting in continuously invertible volatility models

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  • Wintenberger, Olivier
  • Cai, Sixiang

Abstract

We introduce the notion of continuously invertible volatility models that relies on some Lyapunov condition and some regularity condition. We show that it is almost equivalent to the volatilities forecasting efficiency of the parametric inference approach based on the Stochastic Recurrence Equation (SRE) given in Straumann (2005). Under very weak assumptions, we prove the strong consistency and the asymptotic normality of an estimator based on the SRE. From this parametric estimation, we deduce a natural forecast of the volatility that is strongly consistent. We successfully apply this approach to recover known results on univariate and multivariate GARCH type models where our estimator coincides with the QMLE. In the EGARCH(1,1)model, we apply this approach to find a strongly consistence forecast and to prove that our estimator is asymptotically normal when the limiting covariance matrix exists. Finally, we give some encouraging empirical results of our approach on simulations and real data.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 31767.

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Date of creation: 20 Jun 2011
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Handle: RePEc:pra:mprapa:31767

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Keywords: Invertibility; volatility models; parametric estimation; strong consistency; asymptotic normality; asymmetric GARCH; exponential GARCH; stochastic recurrence equation; stationarity;

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  1. Andrew Patton, 2006. "Volatility Forecast Comparison using Imperfect Volatility Proxies," Research Paper Series 175, Quantitative Finance Research Centre, University of Technology, Sydney.
  2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
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  10. Brandt, Michael W. & Jones, Christopher S., 2006. "Volatility Forecasting With Range-Based EGARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 470-486, October.
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  14. 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.
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Cited by:
  1. Francq, Christian & Wintenberger, Olivier & Zakoïan, Jean-Michel, 2013. "GARCH models without positivity constraints: Exponential or log GARCH?," Journal of Econometrics, Elsevier, vol. 177(1), pages 34-46.

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