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Generalized quasi-maximum likelihood inference for periodic conditionally heteroskedastic models

Abdelhakim Aknouche (), Eid Al-Eid () and Nacer Demouche ()
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Abdelhakim Aknouche: Qassim University
Eid Al-Eid: Qassim University
Nacer Demouche: University of Science and Technology Houari Boumediene

Statistical Inference for Stochastic Processes, 2018, vol. 21, issue 3, 485-511

Abstract: 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 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 asymmetric power GARCH model is given. Moreover, we also 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.

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 (search for similar items in EconPapers)
Date: 2018
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