Negative binomial quasi-likelihood inference for general integer-valued time series models

Aknouche, Abdelhakim and Bendjeddou, Sara and Touche, Nassim (2016): Negative binomial quasi-likelihood inference for general integer-valued time series models. Forthcoming in: Journal of Time Series Analysis

Abstract

Two negative binomial quasi-maximum likelihood estimates (NB-QMLE's) for a general class of count time series models are proposed. The first one is the profile NB-QMLE calculated while arbitrarily fixing the dispersion parameter of the negative binomial likelihood. The second one, termed two-stage NB-QMLE, consists of four stages estimating both conditional mean and dispersion parameters. It is shown that the two estimates are consistent and asymptotically Gaussian under mild conditions. Moreover, the two-stage NB-QMLE enjoys a certain asymptotic efficiency property provided that a negative binomial link function relating the conditional mean and conditional variance is specified. The proposed NB-QMLE's are compared with the Poisson QMLE asymptotically and in finite samples for various well-known particular classes of count time series models such as the (Poisson and negative binomial) Integer GARCH model and the INAR(1) model. Applications to two real datasets are given.

• Item Type: MPRA Paper
• Language: English
• Keywords: Integer-valued time series models, Integer GARCH, Integer AR, Generalized Linear Models, Quasi-likelihood, Geometric QMLE, Negative Binomial QMLE, Poisson QMLE, consistency and asymptotic normality.
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C18 - Methodological Issues: General; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation

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