Inconsistency of the QMLE and asymptotic normality of the weighted LSE for a class of conditionally heteroscedastic
Christian Francq and Jean-Michel Zakoïan
Keywords: Conditional homoscedasticity testing; Inconsistent estimator; Leverage effect; Linear ARCH; Quasi-maximum likelihood;
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.
MPRA working paper