Properties of the QMLE and the Weighted LSE for LARCH(q) Models

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