A Study for Missing Values in PINAR(1)<sub><i>T</i></sub>Processes

Jia, Boting; Wang, Dehui; Zhang, Haixiang

doi:10.1080/03610926.2012.717664

Cited by 9 publications

(3 citation statements)

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“…Motivated by this thought, several interpolation methods can be considered. For instance, Andersson and Karlis [2] proposed imputation based on the bridge imputation (BI), Jia et al [10] considered subgroup mean (SM) imputation. For ease of description, we assume the interpolated value of x n−1 is x * n−1 = (x * 0 , x * 1 , ..., x * n−1 ), where x * i−1 be the interpolation value if δ i−1 = 0 and x * i−1 = x i−1 (i = 1, 2, ..., n) otherwise.…”

Section: First-step Imputation Of Missing Datamentioning

confidence: 99%

“…Rubin [21] introduced the statistical inference of response mechanism named missing at random (MAR); Little and Rubin [15] studied the propensity and statistical inference for both ignorable and nonignorable missing data in general regressive model. Ignorable missing data has been widespreadly concerned in time series, Pourahmadi [19] proposed an interpolation algorithm handling missing data in stationary time series; Andersson and Karlis [2] studied the statistical inference of missing data based on imputation in INAR(1) model; Jia et al [10] made some researches of ignorable missing data in PINAR(1) T processes.…”

Section: Introductionmentioning

confidence: 99%

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Imputation-based semiparametric estimation for INAR(1) processes with missing data

Xiong

Wang

2020

Hacettepe Journal of Mathematics and Statistics

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In applied problems parameter estimation with missing data has risen as a hot topic. Imputation for ignorable incomplete data is one of the most popular methods in integervalued time series. For data missing not at random (MNAR), estimators directly derived by imputation will lead results that is sensitive to the failure of the effectiveness. In view of the first-order integer-valued autoregressive (INAR(1)) processes with MNAR response mechanism, we consider an imputation based semiparametric method, which recommends the complete auxiliary variable of Yule-Walker equation. Asymptotic properties of relevant estimators are also derived. Some simulation studies are conducted to verify the effectiveness of our estimators, and a real example is also presented as an illustration.

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Section: First-step Imputation Of Missing Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Imputation-based semiparametric estimation for INAR(1) processes with missing data

Xiong

Wang

2020

Hacettepe Journal of Mathematics and Statistics

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“…There are researchers also established INAR(1) models based binomial thinning for a class of renew sequences and gave the statistical inferences of the model [10]. They has considered an INAR(1) model with binomial thinning for missing data and obtained some properties of the model [11]. At present, few people have studied the case of all kinds of dispersed data by considering innovation of the INAR(1) model based on binomial thinning operator.…”

Section: Introductionmentioning

confidence: 99%

A New Integer-Valued Auto-Regressive Model Based on Binomial Thinning Operator

Zhang¹,

Fan²

2018

Topics in Chemical &Amp; Material Engineering

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The integer-valued time series appears in many areas of real life, for example, medical care, economics, transportation, insurance, finance, and so on. Especially, we are in the big data period and all kinds of dispersed integer-valued data may appear everyday. The thinning operator is the main method to study the integer-valued time series. In this paper, we propose a new stationary integer-valued first-order auto-regressive (INAR(1)) model based on binomial thinning operator. The model is constructed by considering the innovation to fit different dispersed data. The definition and statistical properties of the model are given. The maximum likelihood method is applied to estimate the parameters. We considered one specific model, in which the innovation follows geometric distribution, which can deal with over-dispersed integer-valued time series data. The performance of CML estimators are evaluated by simulation study. An application is given to an offence data in Track 1706 in Pittsburgh.

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