Inconsistency of the MLE and inference based on weighted LS for LARCH models

Christian Francq and Jean-Michel Zakoian

Abstract: This paper considers a class of finite-order autoregressive linear ARCH models. The model captures the leverage effect, allows the volatility to be arbitrarily close to zero and to reach its minimum for non-zero innovations, and is appropriate for long-memory modeling when infinite orders are allowed. However, the (quasi-)maximum likelihood estimator is, in general, inconsistent. A self-weighted least-squares estimator is proposed and is shown to be asymptotically normal. A score test for conditional homoscedasticity and diagnostic portmanteau tests are developed. Their performance is illustrated via simulation experiments. It is also investigated whether stock market returns exhibit some of the characteristic features of the linear ARCH model.

Keywords: C22; C12; C13; C52; Conditional homoscedasticity testing; Leverage effect; Linear ARCH; Quasi-maximum likelihood; Weighted least-squares (search for similar items in EconPapers)
Date: 2010-09-15
Note: View the original document on HAL open archive server: https://hal.science/hal-00732536
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Citations: View citations in EconPapers (13)

Published in Econometrics, 2010, 159 (1), pp.151. ⟨10.1016/j.jeconom.2010.05.003⟩

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Journal Article: Inconsistency of the MLE and inference based on weighted LS for LARCH models (2010)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00732536

DOI: 10.1016/j.jeconom.2010.05.003

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