Title: Asymptotic Theory for M-estimators in general autoregressive conditional heteroscedasticity models
Abstract: Since the introduction of the autoregressive conditional heteroscedastic model (ARCH) and its successful application to the variance of the UK's inflation rate by Engle (1982), there has been a growing interest in these models. Especially, the extension to the linear GARCH (LGARCH) model of Bollerslev (1986) has made it possible to capture many characteristics of financial data with one single model. Recently, various extensions of LGARCH model has been proposed and can be summarized in the class of augmented GARCH models. The present work studies asymptotic properties of M-estimators for the unknown parameters of these models. Since in practice the quasi-maximum likelihood estimator (QMLE) and the least absolute deviation estimator (LADE) are by far the most popular ones, the work focusses on these two examples of M-estimators. In particular, conditions are identified under which both estimators are consistent and asymptotically normal in polynomial GARCH models and the EGARCH model. The finite sample behaviour is studied and it can be concluded that the heavier the tails of the error distribution the better performs the LADE compared to the QMLE. Finally, the developed theory is applied to estimate the volatility of the DAX30 index and to calculate the one-day-ahead Value-at-Risk for the DAX30 index. It can be seen that the EGARCH model gives the best fit and is therefore more appropriate to other models.
Publication Year: 2013
Publication Date: 2013-01-01
Language: en
Type: article
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