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.
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This effect, typically observed on most stock returns series, means that negative returns have more impact on the volatility than positive returns of the same magnitude.
Indeed, as remarked by a referee, a practitioner is essentially faced by three choices: (a) leave returns untransformed, i.e., set \(c = 1\), (b) express returns in terms of percentages, i.e., set \(c = 100\), or (c) express returns in terms of basis points, i.e., set \(c = 10,000\). Clearly, it is desirable that the dynamics of the volatility model be not affected by the choice of c.
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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.
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Francq, C., Wintenberger, O. & Zakoïan, JM. Goodness-of-fit tests for Log-GARCH and EGARCH models. TEST 27, 27–51 (2018). https://doi.org/10.1007/s11749-016-0506-2
- LM tests
- Invertibility of time series models
- Portmanteau tests
- Quasi-maximum likelihood
Mathematics Subject Classification