Goodness-of-fit tests for extended Log-GARCH models and specification tests against the EGARCH

Christian Francq (1) , Olivier Wintenberger (2, 3) , Jean-Michel Zakoïan (1)

1 LFA - Laboratoire de Finance Assurance
2 LSTA - Laboratoire de Statistique Théorique et Appliquée
3 UCPH - University of Copenhagen = Københavns Universitet

This paper studies goodness of fit tests and specification tests for an extension of the log-GARCH model which is stable by scaling. A Lagrange-Multiplier test is derived for testing the null assumption of extended log-GARCH against more general formulations including the Exponential GARCH (EGARCH). The null assumption of an EGARCH is also tested. Portmanteau goodness-of-fit tests are developed for the extended log-GARCH. Simulations illustrating the theoretical results and an application to real financial data are proposed.

Mots clés: EGARCH; LM tests; Invertibility of time series models; log-GARCH; Portmanteau tests; Quasi-Maximum Likelihood

Domaines: Statistiques [math.ST]

Christian Francq, Olivier Wintenberger, Jean-Michel Zakoïan. Goodness-of-fit tests for extended Log-GARCH models and specification tests against the EGARCH. 2016. ⟨hal-01258922v1⟩