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This paper establishes consistency and asymptotic normality of the generalized quasi-maximum likelihood estimate (GQM LE) for a general class of periodic conditionally heteroskedastic time series models (P CH). In this class of models, the volatility is expressed as a measurable function of the in…nite 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 GQM LE 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 GQM LE to the prediction of power problem in a one-step framework and to P CH models with complex periodic patterns such as high frequency seasonality and non-integer seasonality.Keywords: Periodic conditionally heteroskedastic models, periodic asymmetric power GARCH, generalized QM L estimation, consistency and asymptotic normality, prediction of powers, high frequency periodicity, non-integer periodicity.

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Generalized quasi-maximum likelihood inference for periodic conditionally heteroskedastic models

Aknouche

Al-Eid

Demouche

2017

Stat Inference Stoch Process

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Power periodic threshold GARCH model: Structure and estimation

Guerbyenne

Kessira

2018

Communications in Statistics - Theory and Methods

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Bayesian analysis of periodic asymmetric power GARCH models

Aknouche

Demmouche

Dimitrakopoulos

et al. 2019

Studies in Nonlinear Dynamics &Amp; Econometrics

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In this paper, we set up a generalized periodic asymmetric power GARCH (PAP-GARCH) model whose coefficients, power, and innovation distribution are periodic over time. We first study its properties, such as periodic ergodicity, finiteness of moments and tail behavior of the marginal distributions. Then, we develop an MCMC algorithm, based on the Griddy-Gibbs sampler, under various distributions of the innovation term (Gaussian, Student-t, mixed Gaussian-Student-t). To assess our estimation method we conduct volatility and Value-at-Risk forecasting. Our model is compared against other competing models via the Deviance Information Criterion (DIC). The proposed methodology is applied to simulated and real data.

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Weighted least squares-based inference for stable and unstable threshold power ARCH processes

Cited by 3 publications

References 12 publications

Generalized quasi-maximum likelihood inference for periodic conditionally heteroskedastic models

Generalized quasi-maximum likelihood inference for periodic conditionally heteroskedastic models

Power periodic threshold GARCH model: Structure and estimation

Bayesian analysis of periodic asymmetric power GARCH models

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