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
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.
