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.*

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## 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 |
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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; 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 |

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.uni-muenchen.de/id/eprint/15147 |