Quasilikelihood and quasi-maximum likelihood for GARCH-type processes: Estimating function approach

Hwang, Sun Young; Choi, M.S.; Yeo, In‐Kwon

doi:10.1016/j.jkss.2014.01.005

Cited by 8 publications

(5 citation statements)

References 9 publications

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“… be a sample of observations from the FM-AR or FM-GARCH model. The quasi-likelihood function of the parameter θ is given by [9] ( ) (…”

Section: Feature Selection Methodsmentioning

confidence: 99%

Variable Selection in Finite Mixture of Time-Varying Regression Models

Liu¹,

Ye²

2020

APM

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In this paper, we research the regression problem of time series data from heterogeneous populations on the basis of the finite mixture regression model. We propose two finite mixed time-varying regression models to solve this. A regularization method for variable selection of the models is proposed, which is a mixture of the appropriate penalty functions and 2 l penalty. A Block-wise minimization maximization (MM) algorithm is used for maximum penalized log quasi-likelihood estimation of these models. The procedure is illustrated by analyzing simulations and with an application to analyze the behavior of urban vehicular traffic of the city of São Paulo in the period from 14 to 18 December 2009, which shows that the proposed models outperform the FMR models.

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“… be a sample of observations from the FM-AR or FM-GARCH model. The quasi-likelihood function of the parameter θ is given by [9] ( ) (…”

Section: Feature Selection Methodsmentioning

confidence: 99%

Variable Selection in Finite Mixture of Time-Varying Regression Models

Liu¹,

Ye²

2020

APM

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“…Due to the wideness of the generalized structures, it will be appropriate to discuss further QL estimation. We refer to, for instance, Heyde (1997), Hwang et al (2014b) and Lee (2012) for a background on QL and QML in a broader context.…”

Section: Inferential Issuesmentioning

confidence: 99%

“…It is obvious that the QML-estimator reduces to the maximum likelihood (ML) estimator provided the (unknown) true likelihood is indeed Gaussian. It is interesting to note that even when the true likelihood is different from the Gaussian-likelihood, the QML-estimator continues to be consistent and asymptotically normal under some regularity conditions (cf., Straumann and Mikosch, 2006;Francq and Zakoian, 2013;Hwang et al, 2014b).…”

Section: Quasi Likelihood (Ql)mentioning

confidence: 99%

Contemporary review on the bifurcating autoregressive models : Overview and perspectives

Hwang¹

2014

Journal of the Korean Data and Information Science Society

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Since the bifurcating autoregressive (BAR) model was developed by Cowan and Staudte (1986) to analyze cell lineage data, a lot of research has been directed to BAR and its generalizations. Based mainly on the author's works, this paper is concerned with a contemporary review on the BAR in terms of an overview and perspectives. Specifically, bifurcating structure is extended to multi-cast tree and to branching tree structure. The AR(1) time series model of Cowan and Staudte (1986) is generalized to tree structured random processes. Branching correlations between individuals sharing the same parent are introduced and discussed. Various methods for estimating parameters and related asymptotics are also reviewed. Consequently, the paper aims to give a contemporary overview on the BAR model, providing some perspectives to the future works in this area.

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“…It is interesting to note that even when the true likelihood is different from the PL, the PL estimator continues to be consistent and asymptotically normal under some regularity conditions (cf., Gourieroux (1997, Chap. 4), Hwang et al (2013b)). …”

Section: Pseudo-likelihood (Pl)mentioning

confidence: 99%

“…Consequently, it is interesting to note that the PL based on the Gaussian innovation is essentially the same as the QL based on the martingale differences {X 2 t − h t }. See Proposition 1 of Hwang et al (2013b). We also note that the conditional least squares (CL) score is given by…”

Section: Pseudo-likelihood (Pl)mentioning

confidence: 99%