, Volume 27, Issue 1, pp 27–51 | Cite as

Goodness-of-fit tests for Log-GARCH and EGARCH models

  • Christian FrancqEmail author
  • Olivier Wintenberger
  • Jean-Michel Zakoïan
Original Paper


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.


EGARCH LM tests Invertibility of time series models Log-GARCH Portmanteau tests Quasi-maximum likelihood 

Mathematics Subject Classification

62M10 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.

Supplementary material

11749_2016_506_MOESM1_ESM.pdf (211 kb)
Supplementary material 1 (pdf 210 KB)


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Copyright information

© Sociedad de Estadística e Investigación Operativa 2016

Authors and Affiliations

  1. 1.CREST and University of LilleVilleneuve d’Ascq cedexFrance
  2. 2.Universities of Paris 6 and Copenhagen, LSTAParisFrance
  3. 3.CREST and University of LilleMalakoff CedexFrance

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