Goodness-of-fit tests for Log-GARCH and EGARCH models
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This paper studies goodness-of-fit tests and specification tests for an extension of the Log-GARCH model, which is both asymmetric and stable by scaling. A Lagrange-multiplier test is derived for testing the extended Log-GARCH against more general formulations taking the form of combinations of Log-GARCH and exponential GARCH (EGARCH). The null assumption of an EGARCH is also tested. Portmanteau goodness-of-fit tests are developed for the extended Log-GARCH. An application to real financial data is proposed.
KeywordsEGARCH LM tests Invertibility of time series models Log-GARCH Portmanteau tests Quasi-maximum likelihood
Mathematics Subject Classification62M10 62P20
The authors would like to thank the referees for their helpful comments. Christian Francq and Jean-Michel Zakoïan also gratefully acknowledge financial support from the Ecodec Labex.