Francq, Christian and Zakoian, JeanMichel (2009): Inconsistency of the QMLE and asymptotic normality of the weighted LSE for a class of conditionally heteroscedastic models.

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Abstract
This paper considers a class of finiteorder autoregressive linear ARCH models. The model captures the leverage effect, allows the volatility to be zero and to reach its minimum for nonzero innovations, and is appropriate for longmemory modeling when infinite orders are allowed. It is shown that the quasimaximum likelihood estimator is, in general, inconsistent. To solve this problem, we propose a selfweighted leastsquares estimator and show that this estimator is asymptotically normal. Furthermore, a score test for conditional homoscedasticity and diagnostic portmanteau tests are developed. The latter have an asymptotic distribution which is far from the standard chisquare. Simulation experiments are carried out to assess the performance of the proposed estimator.
Item Type:  MPRA Paper 

Original Title:  Inconsistency of the QMLE and asymptotic normality of the weighted LSE for a class of conditionally heteroscedastic models. 
Language:  English 
Keywords:  Conditional homoscedasticity testing; Inconsistent estimator; Leverage effect; Linear ARCH; Quasimaximum likelihood; Weighted leastsquares 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes 
Item ID:  15147 
Depositing User:  Christian Francq 
Date Deposited:  11 May 2009 01:45 
Last Modified:  29 Sep 2019 00:56 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/15147 