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
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
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
In this paper, methods based on ranks and signs for estimating the parameters of thefirst-order integer-valued autoregressive model in the presence of additive outliers are proposed. In particular, we use the robust s...In this paper, methods based on ranks and signs for estimating the parameters of thefirst-order integer-valued autoregressive model in the presence of additive outliers are proposed. In particular, we use the robust sample autocorrelations based on ranks and signsto obtain estimators for the parameters of the Poisson INAR(1) process. The effects ofadditive outliers on the estimates of parameters of integer-valued time series are examined. Some numerical results of the estimators are presented with a discussion of theobtained results. The proposed methods are applied to a dataset concerning the numberof different IP addresses accessing the server of the pages of the Department of Statistics of the University of Würzburg. The results presented here give motivation to use themethodology in practical situations in which Poisson INAR(1) process contains additiveoutliers.展开更多
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.
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.
文摘In this paper, methods based on ranks and signs for estimating the parameters of thefirst-order integer-valued autoregressive model in the presence of additive outliers are proposed. In particular, we use the robust sample autocorrelations based on ranks and signsto obtain estimators for the parameters of the Poisson INAR(1) process. The effects ofadditive outliers on the estimates of parameters of integer-valued time series are examined. Some numerical results of the estimators are presented with a discussion of theobtained results. The proposed methods are applied to a dataset concerning the numberof different IP addresses accessing the server of the pages of the Department of Statistics of the University of Würzburg. The results presented here give motivation to use themethodology in practical situations in which Poisson INAR(1) process contains additiveoutliers.
