2015
DOI: 10.1111/jtsa.12167
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Poisson QMLE of Count Time Series Models

Abstract: International audienceRegularity conditions are given for the consistency of the Poisson quasi-maximum likelihood estimator of the conditional mean parameter of a count time series model. The asymptotic distribution of the estimator is studied when the parameter belongs to the interior of the parameter space and when it lies at the boundary. Tests for the significance of the parameters and for constant conditional mean are deduced. Applications to specific integer-valued autoregressive (INAR) and integer-value… Show more

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Cited by 95 publications
(133 citation statements)
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“…In that algorithm, maximization of the negative binomial likelihood for an estimated dispersion parameter φ and estimation of φ given the estimated regression parameters θ are iterated until convergence. The quasi negative binomial approach has been chosen for simplicity and its usefulness on deriving consistent estimators when the model for λ t has been correctly specified (see also Ahmad and Francq 2016).…”
Section: Estimation and Inferencementioning
confidence: 99%
“…In that algorithm, maximization of the negative binomial likelihood for an estimated dispersion parameter φ and estimation of φ given the estimated regression parameters θ are iterated until convergence. The quasi negative binomial approach has been chosen for simplicity and its usefulness on deriving consistent estimators when the model for λ t has been correctly specified (see also Ahmad and Francq 2016).…”
Section: Estimation and Inferencementioning
confidence: 99%
“…Now an important issue is to estimate the asymptotic variance of pNB‐QMLE. Similar to Ahmad and Francq (), a consistent estimate of the asymptotic variance J r 1 I r J r 1 of the pNB‐QMLE, false θ ^ r , is false J ^ r 1 false I ^ r false J ^ r 1 with false I ^ r = 1 n true t = 1 n () X t false λ ˜ t () false θ ^ r false λ ˜ t () false θ ^ r () r + false λ ˜ t () false θ ^ r 2 false λ ˜ t () false θ ^ r false λ ˜ t () false θ ^ r θ θ . false J ^ r = 1 n true t = 1 n 1 false λ ˜ t () false θ ^ r () r + false λ ˜ t () false θ ^ r …”
Section: Negative Binomial Qmlesmentioning
confidence: 69%
“…Let θ 0 Θ R m ( m N false) be an unknown "true" parameter, and consider a measurable positive real‐valued function λ : N × Θ () 0 , . A general class of count time series models, as proposed by Ahmad and Francq (), is given through an observable integer‐valued stochastic process {} X t , t double-struckZ , which is defined on () normalΩ , scriptF , P with conditional expectation specified as follows: E () | X t F t 1 = λ () X t 1 , X t 2 , . . . ; θ 0 : = λ t () θ 0 : = λ t , t double-struckZ , where F t scriptF is the σ ‐algebra generated by {} X t , X t 1 , . . . . Without any constraints on (2.1), any discrete‐time stochastic process satisfies (2.1).…”
Section: A General Class Of Count Time Series Modelsmentioning
confidence: 99%
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