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Generalized quasi-maximum likelihood inference for periodic conditionally heteroskedastic models

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Listed:
  • Aknouche, Abdelhakim
  • Al-Eid, Eid
  • Demouche, Nacer

Abstract

This paper establishes consistency and asymptotic normality of the generalized quasi-maximum likelihood estimate (GQMLE) for a general class of periodic conditionally heteroskedastic time series models (PCH). In this class of models, the volatility is expressed as a measurable function of the infinite past of the observed process with periodically time-varying parameters, while the innovation of the model is an independent and periodically distributed sequence. In contrast with the aperiodic case, the proposed GQMLE is rather based on S instrumental density functions where S is the period of the model while the corresponding asymptotic variance is in a "sandwich" form. Application to the periodic GARCH and the periodic asymmetric power GARCH model is given. Moreover, we discuss how to apply the GQMLE to the prediction of power problem in a one-step framework and to PCH models with complex periodic patterns such as high frequency seasonality and non-integer seasonality.

Suggested Citation

  • Aknouche, Abdelhakim & Al-Eid, Eid & Demouche, Nacer, 2016. "Generalized quasi-maximum likelihood inference for periodic conditionally heteroskedastic models," MPRA Paper 75770, University Library of Munich, Germany, revised 19 Dec 2016.
  • Handle: RePEc:pra:mprapa:75770
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    File URL: https://mpra.ub.uni-muenchen.de/75894/1/MPRA_paper_75894.pdf
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    References listed on IDEAS

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    Keywords

    Periodic conditionally heteroskedastic models; periodic asymmetric power GARCH; generalized QML estimation; consistency and asymptotic normality; prediction of powers; high frequency periodicity; non-integer periodicity.;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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