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Negative Binomial Quasi‐Likelihood Inference for General Integer‐Valued Time Series Models

Abdelhakim Aknouche · Sara Bendjeddou · Nassim Touche

25 citations0/0 files storedJournal of Time Series Analysis

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Financial Risk and Volatility Modeling Probability and Statistical Research Statistical Distribution Estimation and Applications

Abstract

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.

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References

2006Integer‐Valued GARCH Process 2010GARCH Models 2010A negative binomial integer-valued GARCH model 2008Modelling Time Series Count Data: An Autoregressive Conditional Poisson Model 2011Modeling overdispersed or underdispersed count data with generalized Poisson integer-valued GARCH models 2011Zero-inflated Poisson and negative binomial integer-valued GARCH models 2015Infinitely Divisible Distributions in Integer‐Valued Garch Models 2015Inference and testing for structural change in general Poisson autoregressive models

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