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Negative Binomial Quasi‐Likelihood Inference for General Integer‐Valued Time Series Models
Author(s) -
Aknouche Abdelhakim,
Bendjeddou Sara,
Touche Nassim
Publication year - 2018
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12277
Subject(s) - mathematics , quasi likelihood , negative binomial distribution , count data , series (stratigraphy) , autoregressive conditional heteroskedasticity , poisson distribution , statistics , conditional variance , binomial (polynomial) , econometrics , volatility (finance) , paleontology , biology
Two negative binomial quasi‐maximum likelihood estimates (NB‐QMLEs) 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‐QMLEs 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‐valued GARCH model and the INAR(1) model. Application to a real dataset is given.