Wintenberger, Olivier and Cai, Sixiang (2011): Parametric inference and forecasting in continuously invertible volatility models.

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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.
Item Type:  MPRA Paper 

Original Title:  Parametric inference and forecasting in continuously invertible volatility models 
Language:  English 
Keywords:  Invertibility, volatility models, parametric estimation, strong consistency, asymptotic normality, asymmetric GARCH, exponential GARCH, stochastic recurrence equation, stationarity 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C32  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C53  Forecasting and Prediction Methods ; Simulation Methods C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics 
Item ID:  31767 
Depositing User:  Sixiang CAI 
Date Deposited:  22 Jun 2011 12:36 
Last Modified:  16 Feb 2019 07:18 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/31767 