Quasi-maximum Likelihood Estimation of Periodic Autoregressive, Conditionally Heteroscedastic Time Series PDF Download
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Author: Florian Ziel
Publisher:
ISBN:
Category :
Languages : en
Pages : 17
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Author: Florian Ziel
Publisher:
ISBN:
Category :
Languages : en
Pages : 17
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Author: Abdelhakim Aknouche
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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This article establishes the strong consistency and asymptotic normality (CAN) of the quasi-maximum likelihood estimator (QMLE) for generalized autoregressive conditionally heteroscedastic (GARCH) and autoregressive moving-average (ARMA)-GARCH processes with periodically time-varying parameters. We first give a necessary and sufficient condition for the existence of a strictly periodically stationary solution of the periodic GARCH (PGARCH) equation. As a result, it is shown that the moment of some positive order of the PGARCH solution is finite, under which we prove the strong consistency and asymptotic normality of the QMLE for a PGARCH process without any condition on its moments and for a periodic ARMA-GARCH (PARMA-PGARCH) under mild conditions.
Author: Giuseppe Cavaliere
Publisher:
ISBN:
Category :
Languages : en
Pages : 41
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Author: Daniel Straumann
Publisher:
ISBN: 9788778345219
Category :
Languages : en
Pages : 36
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Author: Ansgar Steland
Publisher: Springer
ISBN: 3319138812
Category : Mathematics
Languages : en
Pages : 479
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Book Description
This volume presents the latest advances and trends in stochastic models and related statistical procedures. Selected peer-reviewed contributions focus on statistical inference, quality control, change-point analysis and detection, empirical processes, time series analysis, survival analysis and reliability, statistics for stochastic processes, big data in technology and the sciences, statistical genetics, experiment design, and stochastic models in engineering. Stochastic models and related statistical procedures play an important part in furthering our understanding of the challenging problems currently arising in areas of application such as the natural sciences, information technology, engineering, image analysis, genetics, energy and finance, to name but a few. This collection arises from the 12th Workshop on Stochastic Models, Statistics and Their Applications, Wroclaw, Poland.
Author: Mirko Armillotta
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Category :
Languages : en
Pages : 0
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We propose a novel estimation approach for a general class of semi-parametric time series models where the conditional expectation is modeled through a parametric function. The proposed class of estimators is based on a Gaussian quasi-likelihood function and it relies on the specification of a parametric pseudo-variance that can contain parametric restrictions with respect to the conditional expectation. The specification of the pseudo-variance and the parametric restrictions follow naturally in observation-driven models with bounds in the support of the observable process, such as count processes and double-bounded time series. We derive the asymptotic properties of the estimators and a validity test for the parameter restrictions. We show that the results remain valid irrespective of the correct specification of the pseudo-variance. The key advantage of the restricted estimators is that they can achieve higher efficiency compared to alternative quasi-likelihood methods that are available in the literature. Furthermore, the testing approach can be used to build specification tests for parametric time series models. We illustrate the practical use of the methodology in a simulation study and two empirical applications featuring integer-valued autoregressive processes, where assumptions on the dispersion of the thinning operator are formally tested, and autoregressions for double-bounded data with application to a realized correlation time series.
Author: Daniel Straumann
Publisher:
ISBN: 9788778345585
Category :
Languages : en
Pages :
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Author: Whitney K. Newey
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ISBN:
Category :
Languages : en
Pages :
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Author: Tim Bollerslev
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Category :
Languages : en
Pages :
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High frequency asset returns generally exhibit time dependent and seasonal clustering of volatility. This paper proposes a new class of models featuring periodicity in conditional heteroskedasticity explicitly designed to capture the repetitive seasonal time variation in the second order moments. The structures of this new class of Periodic ARCH, or P-ARCH, models share many properties with the periodic ARMA processes for the mean. The implicit relation between P-GARCH structures and time-invariant seasonal weak GARCH processes documents how neglected autoregressive conditional heteroskedastic periodicity may give rise to a loss in efficiency. The importance and magnitude of this informational loss are quantified for a variety of loss functions through the use of Monte Carlo simulation methods. An empirical example for the daily bilateral Deutschemark - British Pound spot exchange rate highlights the practical relevance of the new P-GARCH class of models. Extensions to other periodic ARCH structures, including P-IGARCH and P- EGARCH processes along with possible discrete time periodic representations of stochastic volatility models subject to time deformation, are also discussed, along with issues related to multivariate representations and the possibility of common persistence in the seasonal volatility across multiple time series.
Author: Christopher C. Heyde
Publisher: Springer Science & Business Media
ISBN: 0387226796
Category : Mathematics
Languages : en
Pages : 236
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Book Description
The first account in book form of all the essential features of the quasi-likelihood methodology, stressing its value as a general purpose inferential tool. The treatment is rather informal, emphasizing essential principles rather than detailed proofs, and readers are assumed to have a firm grounding in probability and statistics at the graduate level. Many examples of the use of the methods in both classical statistical and stochastic process contexts are provided.
