Parametric inference and forecasting in continuously invertible volatility models
AbstractWe 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 InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 31767.
Date of creation: 20 Jun 2011
Date of revision:
Invertibility; volatility models; parametric estimation; strong consistency; asymptotic normality; asymmetric GARCH; exponential GARCH; stochastic recurrence equation; stationarity;
Find related papers by JEL classification:
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
- C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-07-02 (All new papers)
- NEP-ECM-2011-07-02 (Econometrics)
- NEP-ETS-2011-07-02 (Econometric Time Series)
- NEP-FOR-2011-07-02 (Forecasting)
- NEP-ORE-2011-07-02 (Operations Research)
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- 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.
- Patton, Andrew J., 2011.
"Volatility forecast comparison using imperfect volatility proxies,"
Journal of Econometrics,
Elsevier, vol. 160(1), pages 246-256, January.
- Andrew Patton, 2006. "Volatility Forecast Comparison using Imperfect Volatility Proxies," Research Paper Series 175, Quantitative Finance Research Centre, University of Technology, Sydney.
- Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
- Zaffaroni, Paolo, 2009. "Whittle estimation of EGARCH and other exponential volatility models," Journal of Econometrics, Elsevier, vol. 151(2), pages 190-200, August.
- He, Changli & Ter svirta, Timo & Malmsten, Hans, 2002. "Moment Structure Of A Family Of First-Order Exponential Garch Models," Econometric Theory, Cambridge University Press, vol. 18(04), pages 868-885, August.
- María José Rodríguez & Esther Ruiz, 2009.
"GARCH models with leverage effect : differences and similarities,"
Statistics and Econometrics Working Papers
ws090302, Universidad Carlos III, Departamento de Estadística y Econometría.
- Rodríguez, Mª José & Ruiz, Esther, . "GARCH models with leverage effect : differences and similarities," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/3474, Universidad Carlos III de Madrid.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
- 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.
- Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993.
"On the relation between the expected value and the volatility of the nominal excess return on stocks,"
157, Federal Reserve Bank of Minneapolis.
- Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
- Harvey, A., 2010.
"Exponential Conditional Volatility Models,"
Cambridge Working Papers in Economics
1040, Faculty of Economics, University of Cambridge.
- Marc Potters & Jean-Philippe Bouchaud, 2001. "More stylized facts of financial markets: leverage effect and downside correlations," Science & Finance (CFM) working paper archive 29960, Science & Finance, Capital Fund Management.
- 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.
- Francq, Christian & Zakoïan, Jean-Michel, 2012. "Qml Estimation Of A Class Of Multivariate Asymmetric Garch Models," Econometric Theory, Cambridge University Press, vol. 28(01), pages 179-206, February.
- Francq, Christian & Wintenberger, Olivier & Zakoian, Jean-Michel, 2012. "Garch models without positivity constraints: exponential or log garch?," MPRA Paper 41373, University Library of Munich, Germany.
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