Semiparametric integer‐valued autoregressive models on ℤ

Liu, Zhengwei; Li, Q.; Zhu, Fukang

doi:10.1002/cjs.11621

Cited by 14 publications

(3 citation statements)

References 20 publications

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“…for the design of control charts relying on a fitted INAR(1) model. Another interesting issue for future research is the application of our proposed method on integer-valued autoregressive models on Z, such as those proposed by Kim and Park (2008) or Liu et al (2021).…”

Section: Discussionmentioning

confidence: 99%

Semiparametric estimation of INAR models using roughness penalization

et al. 2022

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Popular models for time series of count data are integer-valued autoregressive (INAR) models, for which the literature mainly deals with parametric estimation. In this regard, a semiparametric estimation approach is a remarkable exception which allows for estimation of the INAR models without any parametric assumption on the innovation distribution. However, for small sample sizes, the estimation performance of this semiparametric estimation approach may be inferior. Therefore, to improve the estimation accuracy, we propose a penalized version of the semiparametric estimation approach, which exploits the fact that the innovation distribution is often considered to be smooth, i.e. two consecutive entries of the PMF differ only slightly from each other. This is the case, for example, in the frequently used INAR models with Poisson, negative binomially or geometrically distributed innovations. For the data-driven selection of the penalization parameter, we propose two algorithms and evaluate their performance. In Monte Carlo simulations, we illustrate the superiority of the proposed penalized estimation approach and argue that a combination of penalized and unpenalized estimation approaches results in overall best INAR model fits.

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Section: Discussionmentioning

confidence: 99%

Semiparametric estimation of INAR models using roughness penalization

et al. 2022

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“…However, the continuous‐valued AR model is unavailable to analyse such time series. A natural way is to use the rounding function, see Kachour and Yao (2009), Kachour (2014) and Liu et al (2021).…”

Section: Introductionmentioning

confidence: 99%

A trinomial difference autoregressive model and its applications

Chen,

Zhang,

Zhu

2023

Stat

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This paper considers the autoregressive modelling problem of ‐valued time series of counts, whose counting sequence consists of −1, 0 and 1. Most existing methods are based on the signed binomial thinning operator and its some extensions, in which the counting sequence consists of 0 and 1, that is, the cases of −1 is ignored. To fill this gap, we first construct the trinomial difference thinning operator and then propose the trinomial difference Z‐valued autoregressive (TDZAR) model and give some stochastic properties. An attractive merit of the TDZAR model is that the incorporated trinomial difference thinning operator makes the conditional maximum likelihood estimate more wieldy and easy. Second, we discuss the two‐step conditional least squares estimate and the conditional maximum likelihood estimate and establish their asymptotic properties of the estimators. Third, the performances of these estimators are compared via simulation study. Finally, we apply the proposed model to a real data set.

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“…nonnegative integer‐valued random variables, which is independent of X t − k for all k ≥1, with E( ε t )= μ ε and

var false(ϵ_{t} false) = σ_{ϵ}^{2}

. Various generalised versions of the INAR model (1) are considered and investigated by appropriately varying the innovations’ distribution and considering different types of the thinning operator, such as Ristić, Bakouch & Nastić (2009), Bourguignon, Rodrigues & Santos‐Neto (2019), Qi, Li & Zhu (2019), Qian, Li & Zhu (2020), Liu, Li & Zhu (2020), Liu, Li & Zhu (2021) and so on. Model (1) can be regarded as a branching process with immigration having a Bernoulli offspring distribution.…”

Section: Introductionmentioning

confidence: 99%

A new minification integer‐valued autoregressive process driven by explanatory variables

Qian

Zhu

2022

Aus NZ J of Statistics

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Summary The discrete minification model based on the modified negative binomial operator, as an extension to the continuous minification model, can be used to describe an extreme value after few increasing values. To make this model more practical and flexible, a new minification integer‐valued autoregressive process driven by explanatory variables is proposed. Ergodicity of the new process is discussed. The estimators of the unknown parameters are obtained via the conditional least squares and conditional maximum likelihood methods, and the asymptotic properties are also established. A testing procedure for checking existence of the explanatory variables is developed. Some Monte Carlo simulations are given to illustrate the finite‐sample performances of the estimators under specification and misspecification and the test, respectively. A real example is applied to illustrate the performance of our model.

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Semiparametric integer‐valued autoregressive models on ℤ

Cited by 14 publications

References 20 publications

Semiparametric estimation of INAR models using roughness penalization

Semiparametric estimation of INAR models using roughness penalization

A trinomial difference autoregressive model and its applications

A new minification integer‐valued autoregressive process driven by explanatory variables

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