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

Qian, Lianyong; Zhu, Fukang

doi:10.1111/anzs.12379

Cited by 6 publications

(2 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These remains topics of future study. Extensions to the models in Chen et al [21], Qian and Zhu [22], Su and Zhu [23] and Zhang et al [7] are similar. Details will be discussed in a future project.…”

Section: Discussionmentioning

confidence: 58%

Two-Threshold-Variable Integer-Valued Autoregressive Model

Zhang,

Zhu,

Chen

2023

Mathematics

Self Cite

View full text Add to dashboard Cite

In the past, most threshold models considered a single threshold variable. However, for some practical applications, models with two threshold variables may be needed. In this paper, we propose a two-threshold-variable integer-valued autoregressive model based on the binomial thinning operator and discuss some of its basic properties, including the mean, variance, strict stationarity, and ergodicity. We consider the conditional least squares (CLS) estimation and discuss the asymptotic normality of the CLS estimator under the known and unknown threshold values. The performances of the CLS estimator are compared via simulation studies. In addition, two real data sets are considered to underline the superior performance of the proposed model.

show abstract

Section: Discussionmentioning

confidence: 58%

Two-Threshold-Variable Integer-Valued Autoregressive Model

Zhang,

Zhu,

Chen

2023

Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Furthermore, the INAR(1) processes with the negative binomial thinning operator are also proposed. See also [10][11][12][13][14] for the relevant study.…”

Section: Introductionmentioning

confidence: 99%

Randomness Test of Thinning Parameters for the NBRCINAR(1) Process

Zhang

2024

Axioms

View full text Add to dashboard Cite

Non-negative integer-valued time series are usually encountered in practice, and a variety of integer-valued autoregressive processes based on various thinning operators are commonly used to model these count data with temporal dependence. In this paper, we consider a first-order integer-valued autoregressive process constructed by the negative binomial thinning operator with random coefficients, to address the problem of constant thinning parameters which might not always accurately represent real-world settings because of numerous external and internal causes. We estimate the model parameters of interest by the two-step conditional least squares method, obtain the asymptotic behaviors of the estimators, and furthermore devise a technique to test the constancy of the thinning parameters, which is essential for determining whether or not the proposed model should consider the parameters’ randomness. The effectiveness and dependability of the suggested approach are illustrated by a series of thorough simulation studies. Finally, two real-world data analysis examples reveal that the suggested approach is very useful and flexible for applications.

show abstract

A novel time‐varying coefficient Poisson difference model driven by observation

Liu,

Wang

2024

Stat

View full text Add to dashboard Cite

This paper studies a novel time‐varying coefficient integer‐valued time series model driven by observation. The model is suitable for modeling negative integer‐valued time series based on the Poisson difference distribution and extended binomial thinning operator. Main methods used to estimate the parameters are the conditional least squares (CLS) and conditional maximum likelihood (CML) methods. This paper also discusses the consistency and asymptotic normality of the estimation results. Likelihood ratio tests are employed to examine the existence of covariate and observation. Numerical simulations are conducted to verify the accuracy and stability of the model. Finally, a real data application is presented to demonstrate the usefulness and adaptability of this newly proposed model.

show abstract

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

Cited by 6 publications

References 28 publications

Two-Threshold-Variable Integer-Valued Autoregressive Model

Two-Threshold-Variable Integer-Valued Autoregressive Model

Randomness Test of Thinning Parameters for the NBRCINAR(1) Process

A novel time‐varying coefficient Poisson difference model driven by observation

Contact Info

Product

Resources

About