Inconsistency of the QMLE and asymptotic normality of the weighted LSE for a class of conditionally heteroscedastic models.

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

Abstract

This paper considers a class of finite-order autoregressive linear ARCH models. The model captures the leverage effect, allows the volatility to be zero and to reach its minimum for non-zero innovations, and is appropriate for long-memory modeling when infinite orders are allowed. It is shown that the quasi-maximum likelihood estimator is, in general, inconsistent. To solve this problem, we propose a self-weighted least-squares 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 chi-square. Simulation experiments are carried out to assess the performance of the proposed estimator.

• Item Type: MPRA Paper
• Language: English
• Keywords: Conditional homoscedasticity testing; Inconsistent estimator; Leverage effect; Linear ARCH; Quasi-maximum likelihood; Weighted least-squares
• 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 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes

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