The asymptotic behaviors for estimators of the drift parameters in the Ornstein-Uhlenbeck process driven by small symmetricα-stable motion are studied in this paper.Based on the discrete observations,the conditional ...The asymptotic behaviors for estimators of the drift parameters in the Ornstein-Uhlenbeck process driven by small symmetricα-stable motion are studied in this paper.Based on the discrete observations,the conditional least squares estimators(CLSEs)of all the parameters involved in the Ornstein–Uhlenbeck process are proposed.We establish the consistency and the asymptotic distributions of our estimators asεgoes to 0 and n goes to∞simultaneously.展开更多
This paper considers the random coefficient autoregressive model with time-functional variance noises,hereafter the RCA-TFV model.We first establish the consistency and asymptotic normality of the conditional least sq...This paper considers the random coefficient autoregressive model with time-functional variance noises,hereafter the RCA-TFV model.We first establish the consistency and asymptotic normality of the conditional least squares estimator for the constant coefficient.The semiparametric least squares estimator for the variance of the random coefficient and the nonparametric estimator for the variance function are constructed,and their asymptotic results are reported.A simulation study is presented along with an analysis of real data to assess the performance of our method in finite samples.展开更多
The binomial autoregressive(BAR(1))process is very useful to model the integer-valued time series data defined on a finite range.It is commonly observed that the autoregressive coefficient is assumed to be a constant....The binomial autoregressive(BAR(1))process is very useful to model the integer-valued time series data defined on a finite range.It is commonly observed that the autoregressive coefficient is assumed to be a constant.To make the BAR(1)model more practical,this paper introduces a new random coefficient binomial autoregressive model,which is driven by covariates.Basic probabilistic and statistical properties of this model are discussed.Conditional least squares and conditional maximum likelihood estimators of the model parameters are derived,and the asymptotic properties are obtained.The performance of these estimators is compared via a simulation study.An application to a real data example is also provided.The results show that the proposed model and methods perform well for the simulations and application.展开更多
基金Key Natural Science Foundation of Anhui Education Commission,China(No.KJ2017A568)Natural Science Foundation of Anhui Province,China(No.1808085MA02)+1 种基金Quality Engineering Project of Anhui Province,China(No.2019jyxm0476)Quality Engineering Project of Bengbu University,China(No.2018JYXML8)。
文摘The asymptotic behaviors for estimators of the drift parameters in the Ornstein-Uhlenbeck process driven by small symmetricα-stable motion are studied in this paper.Based on the discrete observations,the conditional least squares estimators(CLSEs)of all the parameters involved in the Ornstein–Uhlenbeck process are proposed.We establish the consistency and the asymptotic distributions of our estimators asεgoes to 0 and n goes to∞simultaneously.
基金supported by the National Natural Science Foundation of China(Grant No.52338009)the National Science Fund for Distinguished Young Scholars(Grant No.52025085)+4 种基金the Graduate Research Innovation Project of Hunan Province(Grant No.CX20220952)Xiaohui Liu’s research is supported by the NSF of China(Grant No.11971208)the National Social Science Foundation of China(Grant No.21&ZD152)the Outstanding Youth Fund Project of the Science and Technology Department of Jiangxi Province(Grant No.20224ACB211003)the NSF of China(Grant No.92358303).
文摘This paper considers the random coefficient autoregressive model with time-functional variance noises,hereafter the RCA-TFV model.We first establish the consistency and asymptotic normality of the conditional least squares estimator for the constant coefficient.The semiparametric least squares estimator for the variance of the random coefficient and the nonparametric estimator for the variance function are constructed,and their asymptotic results are reported.A simulation study is presented along with an analysis of real data to assess the performance of our method in finite samples.
基金This paper is supported by the National Natural Science Foundation of China(Nos.11871028,11731015,11901053)the Natural Science Foundation of Jilin Province(No.20180101216JC).
文摘The binomial autoregressive(BAR(1))process is very useful to model the integer-valued time series data defined on a finite range.It is commonly observed that the autoregressive coefficient is assumed to be a constant.To make the BAR(1)model more practical,this paper introduces a new random coefficient binomial autoregressive model,which is driven by covariates.Basic probabilistic and statistical properties of this model are discussed.Conditional least squares and conditional maximum likelihood estimators of the model parameters are derived,and the asymptotic properties are obtained.The performance of these estimators is compared via a simulation study.An application to a real data example is also provided.The results show that the proposed model and methods perform well for the simulations and application.
