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.
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number
15147.
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