In this paper, a Negative Binomial (NB) Integer-valued Autoregressive model of order 1, INAR (1), is used to model and forecast the cumulative number of confirmed COVID-19 infected cases in Kenya independently for the...In this paper, a Negative Binomial (NB) Integer-valued Autoregressive model of order 1, INAR (1), is used to model and forecast the cumulative number of confirmed COVID-19 infected cases in Kenya independently for the three waves starting from 14<sup>th</sup> March 2020 to 1<sup>st</sup> February 2021. The first wave was experienced from 14<sup>th</sup> March 2020 to 15<sup>th</sup> September 2020, the second wave from around 15<sup>th</sup> September 2020 to 1<sup>st</sup> February 2021 and the third wave was experienced from 1<sup>st</sup> February 2021 to 3<sup>rd</sup> June 2021. 5, 10, and 15-day-ahead forecasts are obtained for these three waves and the performance of the NB-INAR (1) model analysed.展开更多
This paper proposes a general integer-valued time series (IVTS) model based on the oneproposed by Al-Osh and Alzaid[1]. The model is represented by a construction from differingfrom Al-Osh's INAR(1) model in which...This paper proposes a general integer-valued time series (IVTS) model based on the oneproposed by Al-Osh and Alzaid[1]. The model is represented by a construction from differingfrom Al-Osh's INAR(1) model in which the INAR(1) model is given only formally. Many basicproblems about the model such as stationarity, spectral representation, the strong law of largenumbers, parameter estimation have been discussed. In this paper, we only study the stationarityand spectral representation. The others will be dealt with in another paper.展开更多
In [7], a general integer-valued time series model, the generalization of the model proposedby Al-Osh and Al..id[1], has been proposed. Its stationarity and spectral representation hasbeen investigated. In this paper,...In [7], a general integer-valued time series model, the generalization of the model proposedby Al-Osh and Al..id[1], has been proposed. Its stationarity and spectral representation hasbeen investigated. In this paper, we make a further study of the model. Its strong law of largenumbers and parameter estimstion are obtained. At the end of the paper, we give a few openproblems to be researched further.展开更多
In this paper, we consider the problem of determining the order ofINAR（Q） model on the basis of the Bayesian estimation theory. The Bayesian es-timator for the order is given with respect to a squared-error loss fu...In this paper, we consider the problem of determining the order ofINAR（Q） model on the basis of the Bayesian estimation theory. The Bayesian es-timator for the order is given with respect to a squared-error loss function. The consistency of the estimator is discussed. The results of a simulation study for the estimation method are presented.展开更多
泊松自回归模型假设到达过程为期望与方差相等的泊松分布,但事实上真正的数据生成过程中的到达过程的方差既可以高于期望也可以低于期望.本文提出了基于Katz到达过程(Katz arrivals)的计数数据自回归模型(INAR-Katz:integer valued auto...泊松自回归模型假设到达过程为期望与方差相等的泊松分布,但事实上真正的数据生成过程中的到达过程的方差既可以高于期望也可以低于期望.本文提出了基于Katz到达过程(Katz arrivals)的计数数据自回归模型(INAR-Katz:integer valued autoregressive process with Katz arrivals).并采用蒙特卡罗模拟方法(Monte Carlo simulations)比较了INAR-Katz模型在矩估计以及极大似然估计下的估计准确程度.最后采用INAR-Katz模型对患呼吸系统疾病的急诊就诊人数进行建模,结果显示INAR-Katz模型优于普通泊松模型、PAR模型,具有很好的应用前景.展开更多
In this paper,we develop the quantile regression(QR)estimation for the first-order integer-valued autoregressive(INAR(1))models by defining the smoothing INAR(1)process.Jittering method is used to derive the QR estima...In this paper,we develop the quantile regression(QR)estimation for the first-order integer-valued autoregressive(INAR(1))models by defining the smoothing INAR(1)process.Jittering method is used to derive the QR estimators for the autoregressive coefficient and the quantile of innovations.The consistency and asymptotic normality of the proposed estimators are established.The performances of the proposed estimation procedures are evaluated by Monte Carlo simulations.The results show that the proposed procedures perform well for simulations and a real data application.展开更多
文摘In this paper, a Negative Binomial (NB) Integer-valued Autoregressive model of order 1, INAR (1), is used to model and forecast the cumulative number of confirmed COVID-19 infected cases in Kenya independently for the three waves starting from 14<sup>th</sup> March 2020 to 1<sup>st</sup> February 2021. The first wave was experienced from 14<sup>th</sup> March 2020 to 15<sup>th</sup> September 2020, the second wave from around 15<sup>th</sup> September 2020 to 1<sup>st</sup> February 2021 and the third wave was experienced from 1<sup>st</sup> February 2021 to 3<sup>rd</sup> June 2021. 5, 10, and 15-day-ahead forecasts are obtained for these three waves and the performance of the NB-INAR (1) model analysed.
文摘This paper proposes a general integer-valued time series (IVTS) model based on the oneproposed by Al-Osh and Alzaid[1]. The model is represented by a construction from differingfrom Al-Osh's INAR(1) model in which the INAR(1) model is given only formally. Many basicproblems about the model such as stationarity, spectral representation, the strong law of largenumbers, parameter estimation have been discussed. In this paper, we only study the stationarityand spectral representation. The others will be dealt with in another paper.
文摘In [7], a general integer-valued time series model, the generalization of the model proposedby Al-Osh and Al..id[1], has been proposed. Its stationarity and spectral representation hasbeen investigated. In this paper, we make a further study of the model. Its strong law of largenumbers and parameter estimstion are obtained. At the end of the paper, we give a few openproblems to be researched further.
文摘In this paper, we consider the problem of determining the order ofINAR（Q） model on the basis of the Bayesian estimation theory. The Bayesian es-timator for the order is given with respect to a squared-error loss function. The consistency of the estimator is discussed. The results of a simulation study for the estimation method are presented.
文摘泊松自回归模型假设到达过程为期望与方差相等的泊松分布,但事实上真正的数据生成过程中的到达过程的方差既可以高于期望也可以低于期望.本文提出了基于Katz到达过程(Katz arrivals)的计数数据自回归模型(INAR-Katz:integer valued autoregressive process with Katz arrivals).并采用蒙特卡罗模拟方法(Monte Carlo simulations)比较了INAR-Katz模型在矩估计以及极大似然估计下的估计准确程度.最后采用INAR-Katz模型对患呼吸系统疾病的急诊就诊人数进行建模,结果显示INAR-Katz模型优于普通泊松模型、PAR模型,具有很好的应用前景.
基金supported by National Natural Science Foundation of China(No.11871028,11731015,12001229,11901053)Natural Science Foundation of Jilin Province(No.20180101216JC)。
文摘In this paper,we develop the quantile regression(QR)estimation for the first-order integer-valued autoregressive(INAR(1))models by defining the smoothing INAR(1)process.Jittering method is used to derive the QR estimators for the autoregressive coefficient and the quantile of innovations.The consistency and asymptotic normality of the proposed estimators are established.The performances of the proposed estimation procedures are evaluated by Monte Carlo simulations.The results show that the proposed procedures perform well for simulations and a real data application.
