In this paper, we not only construct the confidence region for parameters in a mixed integer-valued autoregressive process using the empirical likelihood method, but also establish the empirical log-likelihood ratio s...In this paper, we not only construct the confidence region for parameters in a mixed integer-valued autoregressive process using the empirical likelihood method, but also establish the empirical log-likelihood ratio statistic and obtain its limiting distribution. And then, via simulation studies we give coverage probabilities for the parameters of interest. The results show that the empirical likelihood method performs very well.展开更多
To better capture the characteristics of asymmetry and structural fluctuations observed in count time series,this study delves into the application of the quantile regression(QR)method for analyzing and forecasting no...To better capture the characteristics of asymmetry and structural fluctuations observed in count time series,this study delves into the application of the quantile regression(QR)method for analyzing and forecasting nonlinear integer-valued time series exhibiting a piecewise phenomenon.Specifically,we focus on the parameter estimation in the first-order Self-Exciting Threshold Integer-valued Autoregressive(SETINAR(2,1))process with symmetry,asymmetry,and contaminated innovations.We establish the asymptotic properties of the estimator under certain regularity conditions.Monte Carlo simulations demonstrate the superior performance of the QR method compared to the conditional least squares(CLS)approach.Furthermore,we validate the robustness of the proposed method through empirical quantile regression estimation and forecasting for larceny incidents and CAD drug call counts in Pittsburgh,showcasing its effectiveness across diverse levels of data heterogeneity.展开更多
Motivated by the need of modeling and inference for high-order integer-valued threshold time series models,this paper introduces a pth-order two-regime self-excited threshold integer-valued autoregressive(SETINAR(2,p)...Motivated by the need of modeling and inference for high-order integer-valued threshold time series models,this paper introduces a pth-order two-regime self-excited threshold integer-valued autoregressive(SETINAR(2,p))model.Basic probabilistic and statistical properties of the model are discussed.The parameter estimation problem is addressed by means of conditional least squares and conditional maximum likelihood methods.The asymptotic properties of the estimators,including the threshold parameter,are obtained.A method to test the nonlinearity of the underlying process is provided.Some simulation studies are conducted to show the performances of the proposed methods.Finally,an application to the number of people suffering from meningococcal disease in Germany is provided.展开更多
This paper introduces a bivariate hysteretic integer-valued autoregressive(INAR)process driven by a bivariate Poisson innovation.It deals well with the buffered or hysteretic characteristics of the data.Model properti...This paper introduces a bivariate hysteretic integer-valued autoregressive(INAR)process driven by a bivariate Poisson innovation.It deals well with the buffered or hysteretic characteristics of the data.Model properties such as sationarity and ergodicity are studied in detail.Parameter estimation problem is also well address via methods of two-step conditional least squares(CLS)and conditional maximum likelihood(CML).The boundary parameters are estimated via triangular grid searching algorithm.The estimation effect is verified through simulations based on three scenarios.Finally,the new model is applied to the offence counts in New South Wales(NSW),Australia.展开更多
In this article,we study a robust estimation method for a general class of integervalued time series models.The conditional distribution of the process belongs to a broad class of distributions and unlike the classica...In this article,we study a robust estimation method for a general class of integervalued time series models.The conditional distribution of the process belongs to a broad class of distributions and unlike the classical autoregressive framework,the conditional mean of the process also depends on some exogenous covariates.We derive a robust inference procedure based on the minimum density power divergence.Under certain regularity conditions,we establish that the proposed estimator is consistent and asymptotically normal.In the case where the conditional distribution belongs to the exponential family,we provide sufficient conditions for the existence of a stationary and ergodicτ-weakly dependent solution.Simulation experiments are conducted to illustrate the empirical performances of the estimator.An application to the number of transactions per minute for the stock Ericsson B is also provided.展开更多
In this paper,we study a robust estimation method for the observation-driven integervalued time-series models in which the conditional probability mass of current observations is assumed to follow a negative binomial ...In this paper,we study a robust estimation method for the observation-driven integervalued time-series models in which the conditional probability mass of current observations is assumed to follow a negative binomial distribution.Maximum likelihood estimator is highly affected by the outliers.We resort to the minimum density power divergence estimator as a robust estimator and showthat it is strongly consistent and asymptotically normal under some regularity conditions.Simulation results are provided to illustrate the performance of the estimator.An application is performed on data for campylobacteriosis infections.展开更多
Let {X<sub>n</sub>, n≥1} be a sequence of random variables taking values in S={1,2,…} with the joint distribution f（x<sub>1</sub>,…, x<sub>n</sub>）=P（X<sub>1</sub>...Let {X<sub>n</sub>, n≥1} be a sequence of random variables taking values in S={1,2,…} with the joint distribution f（x<sub>1</sub>,…, x<sub>n</sub>）=P（X<sub>1</sub>=x<sub>1</sub>,…, X<sub>n</sub>=x<sub>n</sub>）】0, x<sub>i</sub>∈S,1≤i≤n.（1） It is easy to see that {X<sub>n</sub>, n≥l} are independent and identically distributed iff there exists a probability distibution on展开更多
In this paper,the authors consider the empirical likelihood method for a first-order generalized random coefficient integer-valued autoregressive process.The authors establish the log empirical likelihood ratio statis...In this paper,the authors consider the empirical likelihood method for a first-order generalized random coefficient integer-valued autoregressive process.The authors establish the log empirical likelihood ratio statistic and obtain its limiting distribution.Furthermore,the authors investigate the point estimation,confidence regions and hypothesis testing for the parameters of interest.The performance of empirical likelihood method is illustrated by a simulation study and a real data example.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
Time series of counts observed in practice often exhibit overdispersion or underdispersion,zero inflation and even heavy-tailedness(the tail probabilities are non-negligible or decrease very slowly).In this article,we...Time series of counts observed in practice often exhibit overdispersion or underdispersion,zero inflation and even heavy-tailedness(the tail probabilities are non-negligible or decrease very slowly).In this article,we propose a more flexible integer-valued GARCH model based on the generalized Conway-Maxwell-Poisson distribution to model time series of counts,which offers a unified framework to deal with overdispersed or underdispersed,zero-inflated and heavy-tailed time series of counts.This distribution generalizes the Conway-Maxwell-Poisson distribution by adding a parameter,which plays the role of controlling the length of the tail.We investigate basic properties of the proposed model and obtain estimators of parameters via the conditional maximum likelihood method.The numerical results with both simulated and real data confirm the good performance of the proposed model.展开更多
Abstract Denote by z（p） （resp. Zp） the p localization （resp. p completion） of z. Then we have the canonical inclusion Z（p）→ zp. Let S2n-1（p） be the p-local （2n- 1）-sphere and let B2n（p） be a connected p...Abstract Denote by z（p） （resp. Zp） the p localization （resp. p completion） of z. Then we have the canonical inclusion Z（p）→ zp. Let S2n-1（p） be the p-local （2n- 1）-sphere and let B2n（p） be a connected p-local space satisfying S2n-l（p）≌ΩB2n（p）, then H＊B2n（p）,Z（p）） = Z（p）[U] with ｜u｜ = 2n. Define the degree of a self-map f of B2n（p） to be k E Z（p） such that f＊（u） = ku. Using the theory of integer-valued polynomials we show that there exists a self-map of B2n（p） of degree k if and only if k is an n-th power in Zp.展开更多
The time series model with threshold characteristics under fully observations has been explored intensively in recent years.In this article,several methods are proposed to estimate the parameters of the self-exciting ...The time series model with threshold characteristics under fully observations has been explored intensively in recent years.In this article,several methods are proposed to estimate the parameters of the self-exciting threshold integer-valued autoregressive(SETINAR(2,1))process in the presence of completely random missing data.In order to dispose of the non-equidistance in the observed data,we research the conditional least squares and conditional maximum likelihood inference based on the p-stepahead conditional distribution of incomplete observations;in addition,three kinds of imputation methods are investigated to deal with the missing values for estimating the parameters of interest.Multiple groups of stochastic simulation studies are carried out to compare the proposed approaches.展开更多
Let a,b and n be positive integers withn≥2,f be an integer-valued arithmetic function,and the set S={x_(1),…,x_(n)}of n distinct positive integers be a divisor chain such that x_(1)|x_(2)|⋯|x_(n).We first show that ...Let a,b and n be positive integers withn≥2,f be an integer-valued arithmetic function,and the set S={x_(1),…,x_(n)}of n distinct positive integers be a divisor chain such that x_(1)|x_(2)|⋯|x_(n).We first show that the matrix(f_(a)(S))having f evaluated at the ath power(x_(i),x_(j))^(a) of the greatest common divisor of x_(i) and x_(j) as its i,j-entry divides the GCD matrix(f^(b)(S))in the ring M_(n)(Z)of n×n matrices over integers if and only if f^(b−a)(x_(1))∈Z and(f^(a)(x_(i))−f^(a)(x_(i−1)))divides(f^(b)(x_(i))−f^(b)(x_(i−1)))for any integer i with 2≤i≤n.Consequently,we show that the matrix(f^(a)[S])having f evaluated at the ath power[x_(i),x_(j)]^(a) of the least common multiple of x_(i) and x_(j) as its i,j-entry divides the matrix(f^(b)[S])in the ring M_(n)(Z)if and only if f^(b−a)(x_(n))∈Z and(f^(a)(x_(i))−f^(a)(x_(i−1)))divides(f^(b)(x_(i))−f^(b)(x_(i−1)))for any integer i with2≤i≤n.Finally,we prove that the matrix(f^(a)(S))divides the matrix(f^(b)[S])in the ring M_(n)(Z)if and only if f^(a)(x_(1))|f^(b)(x_(i))and(f^(a)(x_(i))−f^(a)(x_(i−1)))|(f^(b)(x_(i))−f^(b)(x_(i−1)))for any integer i with 2≤i≤n.Our results extend and strengthen the theorems of Hong obtained in 2008.展开更多
基金Supported by National Natural Science Foundation of China(11731015,11571051,J1310022,11501241)Natural Science Foundation of Jilin Province(20150520053JH,20170101057JC,20180101216JC)+2 种基金Program for Changbaishan Scholars of Jilin Province(2015010)Science and Technology Program of Jilin Educational Department during the "13th Five-Year" Plan Period(2016-399)Science and Technology Research Program of Education Department in Jilin Province for the 13th Five-Year Plan(2016213)
文摘In this paper, we not only construct the confidence region for parameters in a mixed integer-valued autoregressive process using the empirical likelihood method, but also establish the empirical log-likelihood ratio statistic and obtain its limiting distribution. And then, via simulation studies we give coverage probabilities for the parameters of interest. The results show that the empirical likelihood method performs very well.
基金supported by Social Science Planning Foundation of Liaoning Province(Grand No.L22ZD065)National Natural Science Foundation of China(Grand Nos.12271231,1247012719,12001229)。
文摘To better capture the characteristics of asymmetry and structural fluctuations observed in count time series,this study delves into the application of the quantile regression(QR)method for analyzing and forecasting nonlinear integer-valued time series exhibiting a piecewise phenomenon.Specifically,we focus on the parameter estimation in the first-order Self-Exciting Threshold Integer-valued Autoregressive(SETINAR(2,1))process with symmetry,asymmetry,and contaminated innovations.We establish the asymptotic properties of the estimator under certain regularity conditions.Monte Carlo simulations demonstrate the superior performance of the QR method compared to the conditional least squares(CLS)approach.Furthermore,we validate the robustness of the proposed method through empirical quantile regression estimation and forecasting for larceny incidents and CAD drug call counts in Pittsburgh,showcasing its effectiveness across diverse levels of data heterogeneity.
基金supported by the National Natural Science Foundation of China(No.11901053)Natural Science Foundation of Jilin Province(No.20220101038JC,20210101149JC)Scientific Research Project of Jilin Provincial Department of Education(No.JJKH20220671KJ).
文摘Motivated by the need of modeling and inference for high-order integer-valued threshold time series models,this paper introduces a pth-order two-regime self-excited threshold integer-valued autoregressive(SETINAR(2,p))model.Basic probabilistic and statistical properties of the model are discussed.The parameter estimation problem is addressed by means of conditional least squares and conditional maximum likelihood methods.The asymptotic properties of the estimators,including the threshold parameter,are obtained.A method to test the nonlinearity of the underlying process is provided.Some simulation studies are conducted to show the performances of the proposed methods.Finally,an application to the number of people suffering from meningococcal disease in Germany is provided.
基金supported by the National Natural Science Foundation of China under Grant Nos.12471249 and 12101417the Natural Science Foundation of Jilin Province under Grant Nos.YDZJ202301ZYTS393 and20220101038JC+1 种基金Postdoctoral Foundation of Jilin Province under Grant No.2023337Scientific Research Project of Jilin Provincial Department of Education under Grant No.JJKH20230665KJ。
文摘This paper introduces a bivariate hysteretic integer-valued autoregressive(INAR)process driven by a bivariate Poisson innovation.It deals well with the buffered or hysteretic characteristics of the data.Model properties such as sationarity and ergodicity are studied in detail.Parameter estimation problem is also well address via methods of two-step conditional least squares(CLS)and conditional maximum likelihood(CML).The boundary parameters are estimated via triangular grid searching algorithm.The estimation effect is verified through simulations based on three scenarios.Finally,the new model is applied to the offence counts in New South Wales(NSW),Australia.
基金supported by the MME-DII center of excellence(ANR-11-LABEX-0023-01)the ANR BREAKRISK:ANR-17-CE26-0001-01+1 种基金the CY Initiative of Excellence(grant“Investissements d’Avenir”ANR-16-IDEX-0008)Project“EcoDep”PSI-AAP2020-0000000013.
文摘In this article,we study a robust estimation method for a general class of integervalued time series models.The conditional distribution of the process belongs to a broad class of distributions and unlike the classical autoregressive framework,the conditional mean of the process also depends on some exogenous covariates.We derive a robust inference procedure based on the minimum density power divergence.Under certain regularity conditions,we establish that the proposed estimator is consistent and asymptotically normal.In the case where the conditional distribution belongs to the exponential family,we provide sufficient conditions for the existence of a stationary and ergodicτ-weakly dependent solution.Simulation experiments are conducted to illustrate the empirical performances of the estimator.An application to the number of transactions per minute for the stock Ericsson B is also provided.
基金supported by National Natural Science Foundation of China(Nos.11871027,11731015)Science and Technology Developing Plan of Jilin Province(No.20170101057JC)Cultivation Plan for Excellent Young Scholar Candidates of Jilin University.
文摘In this paper,we study a robust estimation method for the observation-driven integervalued time-series models in which the conditional probability mass of current observations is assumed to follow a negative binomial distribution.Maximum likelihood estimator is highly affected by the outliers.We resort to the minimum density power divergence estimator as a robust estimator and showthat it is strongly consistent and asymptotically normal under some regularity conditions.Simulation results are provided to illustrate the performance of the estimator.An application is performed on data for campylobacteriosis infections.
文摘Let {X<sub>n</sub>, n≥1} be a sequence of random variables taking values in S={1,2,…} with the joint distribution f（x<sub>1</sub>,…, x<sub>n</sub>）=P（X<sub>1</sub>=x<sub>1</sub>,…, X<sub>n</sub>=x<sub>n</sub>）】0, x<sub>i</sub>∈S,1≤i≤n.（1） It is easy to see that {X<sub>n</sub>, n≥l} are independent and identically distributed iff there exists a probability distibution on
基金supported by the National Natural Science Foundation of China under Grant Nos.11871028 and 11731015。
文摘In this paper,the authors consider the empirical likelihood method for a first-order generalized random coefficient integer-valued autoregressive process.The authors establish the log empirical likelihood ratio statistic and obtain its limiting distribution.Furthermore,the authors investigate the point estimation,confidence regions and hypothesis testing for the parameters of interest.The performance of empirical likelihood method is illustrated by a simulation study and a real data example.
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.
基金the Priority Academic Program Development of Jiangsu Higher Education Institutions and the Teacher’s Research Support Project Foundation of Jiangsu Normal University(No.21XFRS022)National Natural Science Foundation of China(Nos.12271206,11871027)Natural Science Foundation of Jilin Province(No.20210101143JC).
文摘Time series of counts observed in practice often exhibit overdispersion or underdispersion,zero inflation and even heavy-tailedness(the tail probabilities are non-negligible or decrease very slowly).In this article,we propose a more flexible integer-valued GARCH model based on the generalized Conway-Maxwell-Poisson distribution to model time series of counts,which offers a unified framework to deal with overdispersed or underdispersed,zero-inflated and heavy-tailed time series of counts.This distribution generalizes the Conway-Maxwell-Poisson distribution by adding a parameter,which plays the role of controlling the length of the tail.We investigate basic properties of the proposed model and obtain estimators of parameters via the conditional maximum likelihood method.The numerical results with both simulated and real data confirm the good performance of the proposed model.
文摘Abstract Denote by z（p） （resp. Zp） the p localization （resp. p completion） of z. Then we have the canonical inclusion Z（p）→ zp. Let S2n-1（p） be the p-local （2n- 1）-sphere and let B2n（p） be a connected p-local space satisfying S2n-l（p）≌ΩB2n（p）, then H＊B2n（p）,Z（p）） = Z（p）[U] with ｜u｜ = 2n. Define the degree of a self-map f of B2n（p） to be k E Z（p） such that f＊（u） = ku. Using the theory of integer-valued polynomials we show that there exists a self-map of B2n（p） of degree k if and only if k is an n-th power in Zp.
基金supported by National Natural Science Foundation of China (Nos.11871028,11731015,11901053).
文摘The time series model with threshold characteristics under fully observations has been explored intensively in recent years.In this article,several methods are proposed to estimate the parameters of the self-exciting threshold integer-valued autoregressive(SETINAR(2,1))process in the presence of completely random missing data.In order to dispose of the non-equidistance in the observed data,we research the conditional least squares and conditional maximum likelihood inference based on the p-stepahead conditional distribution of incomplete observations;in addition,three kinds of imputation methods are investigated to deal with the missing values for estimating the parameters of interest.Multiple groups of stochastic simulation studies are carried out to compare the proposed approaches.
基金supported partially by Doctoral Research Initiation FundProjectof PanzhihuaUniversity(bkqj2019050).
文摘Let a,b and n be positive integers withn≥2,f be an integer-valued arithmetic function,and the set S={x_(1),…,x_(n)}of n distinct positive integers be a divisor chain such that x_(1)|x_(2)|⋯|x_(n).We first show that the matrix(f_(a)(S))having f evaluated at the ath power(x_(i),x_(j))^(a) of the greatest common divisor of x_(i) and x_(j) as its i,j-entry divides the GCD matrix(f^(b)(S))in the ring M_(n)(Z)of n×n matrices over integers if and only if f^(b−a)(x_(1))∈Z and(f^(a)(x_(i))−f^(a)(x_(i−1)))divides(f^(b)(x_(i))−f^(b)(x_(i−1)))for any integer i with 2≤i≤n.Consequently,we show that the matrix(f^(a)[S])having f evaluated at the ath power[x_(i),x_(j)]^(a) of the least common multiple of x_(i) and x_(j) as its i,j-entry divides the matrix(f^(b)[S])in the ring M_(n)(Z)if and only if f^(b−a)(x_(n))∈Z and(f^(a)(x_(i))−f^(a)(x_(i−1)))divides(f^(b)(x_(i))−f^(b)(x_(i−1)))for any integer i with2≤i≤n.Finally,we prove that the matrix(f^(a)(S))divides the matrix(f^(b)[S])in the ring M_(n)(Z)if and only if f^(a)(x_(1))|f^(b)(x_(i))and(f^(a)(x_(i))−f^(a)(x_(i−1)))|(f^(b)(x_(i))−f^(b)(x_(i−1)))for any integer i with 2≤i≤n.Our results extend and strengthen the theorems of Hong obtained in 2008.
