Inconsistency of the QMLE and asymptotic normality of the weighted LSE for a class of conditionally heteroscedastic models
AbstractThis 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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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 15147.
Date of creation: 2009
Date of revision:
Conditional homoscedasticity testing; Inconsistent estimator; Leverage effect; Linear ARCH; Quasi-maximum likelihood; Weighted least-squares;
Find related papers by JEL classification:
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-05-16 (All new papers)
- NEP-ECM-2009-05-16 (Econometrics)
- NEP-ETS-2009-05-16 (Econometric Time Series)
- NEP-ORE-2009-05-16 (Operations Research)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Tim Bollerslev, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
EERI Research Paper Series
EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
- Beran, Jan, 2006. "On location estimation for LARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1766-1782, September.
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