Invertibility is one of the desirable properties of moving average processes. This study derives consequences of the invertibility condition on the parameters of a moving average process of order three. The study also...Invertibility is one of the desirable properties of moving average processes. This study derives consequences of the invertibility condition on the parameters of a moving average process of order three. The study also establishes the intervals for the first three autocorrelation coefficients of the moving average process of order three for the purpose of distinguishing between the process and any other process (linear or nonlinear) with similar autocorrelation structure. For an invertible moving average process of order three, the intervals obtained are , -0.5ρ2ρ1<0.5.展开更多
Assume that{a_(i),−∞<i<∞}is an absolutely summable sequence of real numbers.We establish the complete q-order moment convergence for the partial sums of moving average processes{X_(n)=Σ_(i=−∞)^(∞)a_(i)Y_(i+...Assume that{a_(i),−∞<i<∞}is an absolutely summable sequence of real numbers.We establish the complete q-order moment convergence for the partial sums of moving average processes{X_(n)=Σ_(i=−∞)^(∞)a_(i)Y_(i+n),n≥1}under some proper conditions,where{Yi,-∞<i<∞}is a doubly infinite sequence of negatively dependent random variables under sub-linear expectations.These results extend and complement the relevant results in probability space.展开更多
In this paper,we obtained complete qth-moment convergence of the moving average processes,which is generated by m-WOD moving random variables.The results in this article improve and extend the results of the moving av...In this paper,we obtained complete qth-moment convergence of the moving average processes,which is generated by m-WOD moving random variables.The results in this article improve and extend the results of the moving average process.mWOD random variables include WOD,m-NA,m-NOD and mEND random variables,so the results in the paper also promote the corresponding ones in WOD,m-NA,m-NOD,m-END random variables.展开更多
Based on the asymptotically almost negatively associated(AANA) random variables, we investigate the complete moment convergence for a moving average process under the moment condition E[Y log(1 + Y)] < ∞. As an ap...Based on the asymptotically almost negatively associated(AANA) random variables, we investigate the complete moment convergence for a moving average process under the moment condition E[Y log(1 + Y)] < ∞. As an application, Marcinkiewicz-Zygmundtype strong law of large numbers for this moving average process is presented in this paper.展开更多
In this paper, the least square estimator in the problem of multiple change points estimation is studied. Here, the moving-average processes of ALNQD sequence in the mean shifts are discussed. When the number of chang...In this paper, the least square estimator in the problem of multiple change points estimation is studied. Here, the moving-average processes of ALNQD sequence in the mean shifts are discussed. When the number of change points is known, the rate of convergence of change-points estimation is derived. The result is also true for p-mixing, φ-mixing, a-mixing, associated and negatively associated sequences under suitable conditions.展开更多
In this paper, we discuss the precise asymptotics of moving-average process Xt =∞∑j=0 ajEt-j under some suitable conditions, where {εt, t∈ Z} is a sequence j=0 of stationary ALNQD random variables with mean zeros...In this paper, we discuss the precise asymptotics of moving-average process Xt =∞∑j=0 ajEt-j under some suitable conditions, where {εt, t∈ Z} is a sequence j=0 of stationary ALNQD random variables with mean zeros and finite variances.展开更多
In the process of large-scale,grid-connected wind power operations,it is important to establish an accurate probability distribution model for wind farm fluctuations.In this study,a wind power fluctuation modeling met...In the process of large-scale,grid-connected wind power operations,it is important to establish an accurate probability distribution model for wind farm fluctuations.In this study,a wind power fluctuation modeling method is proposed based on the method of moving average and adaptive nonparametric kernel density estimation(NPKDE)method.Firstly,the method of moving average is used to reduce the fluctuation of the sampling wind power component,and the probability characteristics of the modeling are then determined based on the NPKDE.Secondly,the model is improved adaptively,and is then solved by using constraint-order optimization.The simulation results show that this method has a better accuracy and applicability compared with the modeling method based on traditional parameter estimation,and solves the local adaptation problem of traditional NPKDE.展开更多
The polynomial matrix using the block coefficient matrix representation auto-regressive moving average(referred to as the PM-ARMA)model is constructed in this paper for actively controlled multi-degree-of-freedom(MDOF...The polynomial matrix using the block coefficient matrix representation auto-regressive moving average(referred to as the PM-ARMA)model is constructed in this paper for actively controlled multi-degree-of-freedom(MDOF)structures with time-delay through equivalently transforming the preliminary state space realization into the new state space realization.The PM-ARMA model is a more general formulation with respect to the polynomial using the coefficient representation auto-regressive moving average(ARMA)model due to its capability to cope with actively controlled structures with any given structural degrees of freedom and any chosen number of sensors and actuators.(The sensors and actuators are required to maintain the identical number.)under any dimensional stationary stochastic excitation.展开更多
The m-widely orthant dependent(m-WOD)sequences are very weak dependent random variables.In the paper,the authors investigate the moving average processes,which is generated by m-WOD random variables.By using the tail ...The m-widely orthant dependent(m-WOD)sequences are very weak dependent random variables.In the paper,the authors investigate the moving average processes,which is generated by m-WOD random variables.By using the tail cut technique and maximum moment inequality of the m-WOD random variables,moment complete convergence and complete convergence of the maximal partial sums for the moving average processes are obtained,the results generalize and improve some corresponding results of the existing literature.展开更多
The present paper first shows that, without any dependent structure assumptions for a sequence of random variables, the refined results of the complete convergence for the sequence is equivalent to the corresponding c...The present paper first shows that, without any dependent structure assumptions for a sequence of random variables, the refined results of the complete convergence for the sequence is equivalent to the corresponding complete moment convergence of the sequence. Then this paper investigates the convergence rates and refined convergence rates （or complete moment convergence） for probabilities of moderate deviations of moving average processes. The results in this paper extend and generalize some well-known results.展开更多
Let {εt;t ∈ Z} be a sequence of m-dependent B-valued random elements with mean zeros and finite second moment. {a3;j ∈ Z} is a sequence of real numbers satisfying ∑j=-∞^∞｜aj｜ 〈 ∞. Define a moving average pro...Let {εt;t ∈ Z} be a sequence of m-dependent B-valued random elements with mean zeros and finite second moment. {a3;j ∈ Z} is a sequence of real numbers satisfying ∑j=-∞^∞｜aj｜ 〈 ∞. Define a moving average process Xt = ∑j=-∞^∞aj＋tEj,t ≥ 1, and Sn = ∑t=1^n Xt,n ≥ 1. In this article, by using the weak convergence theorem of { Sn/√ n _〉 1}, we study the precise asymptotics of the complete convergence for the sequence {Xt; t ∈ N}.展开更多
The bullwhip effect in a multistage supply chain was analyzed using sophisticated stationary forecasts (third order moving average and third order exponential smoothing forecasts). The third order exponential smoothin...The bullwhip effect in a multistage supply chain was analyzed using sophisticated stationary forecasts (third order moving average and third order exponential smoothing forecasts). The third order exponential smoothing and third order moving average forecasts sometimes have a variance reducing effect on the supply chain.In a supply chain with positively correlated or independent and identically distributed (i.i.d) demands, the order variance based on simple moving average forecast (or simple exponential smoothing forecast) is larger than the order variance based on second order moving average forecast (or second order exponential smoothing forecast),and the order variance based on second order moving average forecast( or second order exponential smoothing forecast) is larger than the order variance based on third order moving average forecast( or third order exponential smoothing forecast). In addition, for i.i.d demands, third order exponential smoothing forecast leads to a larger variation than third order moving average forecast.展开更多
In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai＋kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables w...In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai＋kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞） is an absolutely solutely summable sequence of real numbers.展开更多
Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are...Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are discussed. We also discuss complete convergence for the moving average processes underB-valued martingale differences assumption.展开更多
In this paper we discuss the least-square estimator of the unknown change point in a mean shift for moving-average processes of ALNQD sequence. The consistency and the rate of convergence for the estimated change poin...In this paper we discuss the least-square estimator of the unknown change point in a mean shift for moving-average processes of ALNQD sequence. The consistency and the rate of convergence for the estimated change point are established. The asymptotic distribution for the change point estimator is obtained. The results are also true for ρ-mixing, φ-mixing, α-mixing sequences under suitable conditions. These results extend those of Bai, who studied the mean shift point of a linear process of i.i.d, variables, and the condition ∑j=0^∞j｜aj｜ 〈 ∞ in Bai is weakened to ∑j=0^∞｜aj｜〈∞.展开更多
Consistent high-quality and defect-free production is the demand of the day. The product recall not only increases engineering and manufacturing cost but also affects the quality and the reliability of the product in ...Consistent high-quality and defect-free production is the demand of the day. The product recall not only increases engineering and manufacturing cost but also affects the quality and the reliability of the product in the eye of users. The monitoring and improvement of a manufacturing process are the strength of statistical process control. In this article we propose a process monitoring memory-based scheme for continuous data under the assumption of normality to detect small non-random shift patterns in any manufacturing or service process.The control limits for the proposed scheme are constructed. The in-control and out-of-control average run length(AVL) expressions have been derived for the performance evaluation of the proposed scheme. Robustness to non-normality has been tested after simulation study of the run length distribution of the proposed scheme, and the comparisons with Shewhart and exponentially weighted moving average(EWMA) schemes are presented for various gamma and t-distributions. The proposed scheme is effective and attractive as it has one design parameter which differentiates it from the traditional schemes. Finally, some suggestions and recommendations are made for the future work.展开更多
A novel nonlinear combination process monitoring method was proposed based on techniques with memo- ry effect （multivariate exponentially weighted moving average （MEWMA）） and kernel independent component analysis ...A novel nonlinear combination process monitoring method was proposed based on techniques with memo- ry effect （multivariate exponentially weighted moving average （MEWMA）） and kernel independent component analysis （KICA）. The method was developed for dealing with nonlinear issues and detecting small or moderate drifts in one or more process variables with autocorrelation. MEWMA charts use additional information from the past history of the process for keeping the memory effect of the process behavior trend. KICA is a recently devel- oped statistical technique for revealing hidden, nonlinear statistically independent factors that underlie sets of mea- surements and it is a two-phase algorithm., whitened kernel principal component analysis （KPCA） plus indepen- dent component analysis （ICA）. The application to the fluid catalytic cracking unit （FCCU） simulated process in- dicates that the proposed combined method based on MEWMA and KICA can effectively capture the nonlinear rela- tionship and detect small drifts in process variables. Its performance significantly outperforms monitoring method based on ICA, MEWMA-ICA and KICA, especially for lonu-term performance deterioration.展开更多
文摘Invertibility is one of the desirable properties of moving average processes. This study derives consequences of the invertibility condition on the parameters of a moving average process of order three. The study also establishes the intervals for the first three autocorrelation coefficients of the moving average process of order three for the purpose of distinguishing between the process and any other process (linear or nonlinear) with similar autocorrelation structure. For an invertible moving average process of order three, the intervals obtained are , -0.5ρ2ρ1<0.5.
基金Supported by the Academic Achievement Re-cultivation Projects of Jingdezhen Ceramic University(Grant Nos.215/20506341215/20506277)the Doctoral Scientific Research Starting Foundation of Jingdezhen Ceramic University(Grant No.102/01003002031)。
文摘Assume that{a_(i),−∞<i<∞}is an absolutely summable sequence of real numbers.We establish the complete q-order moment convergence for the partial sums of moving average processes{X_(n)=Σ_(i=−∞)^(∞)a_(i)Y_(i+n),n≥1}under some proper conditions,where{Yi,-∞<i<∞}is a doubly infinite sequence of negatively dependent random variables under sub-linear expectations.These results extend and complement the relevant results in probability space.
基金Supported by the Academic Funding Projects for Top Talents in Universities of Anhui Province(gxbj ZD2022067,gxbj ZD2021078)the Philosophy and Social Sciences Planning Project of Anhui Province(AHSKY2018D98)。
文摘In this paper,we obtained complete qth-moment convergence of the moving average processes,which is generated by m-WOD moving random variables.The results in this article improve and extend the results of the moving average process.mWOD random variables include WOD,m-NA,m-NOD and mEND random variables,so the results in the paper also promote the corresponding ones in WOD,m-NA,m-NOD,m-END random variables.
基金Supported by the National Natural Science Foundation of China（11501005, 11526033） Supported by the Natural Science Foundation of Anhui Province（1408085QA02, 1508085J06, 1608085QA02）+3 种基金 Supported by the Provincial Natural Science Research Project of Anhui Colleges（KJ2014A020, KJ2015A065） Supported by the Quality Engineering Project of Anhui Province（2015jyxm054） Supported by the Students Science Research Training Program of Anhui University（KYXL2014016, KYXL2014013） Supported by the Applied Teaching Model Curriculum of Anhui University（XJYYKC1401, ZLTS2015053）
文摘Based on the asymptotically almost negatively associated(AANA) random variables, we investigate the complete moment convergence for a moving average process under the moment condition E[Y log(1 + Y)] < ∞. As an application, Marcinkiewicz-Zygmundtype strong law of large numbers for this moving average process is presented in this paper.
基金Supported by the National Natural Science Foundation of China（10471126）.
文摘In this paper, the least square estimator in the problem of multiple change points estimation is studied. Here, the moving-average processes of ALNQD sequence in the mean shifts are discussed. When the number of change points is known, the rate of convergence of change-points estimation is derived. The result is also true for p-mixing, φ-mixing, a-mixing, associated and negatively associated sequences under suitable conditions.
文摘In this paper, we discuss the precise asymptotics of moving-average process Xt =∞∑j=0 ajEt-j under some suitable conditions, where {εt, t∈ Z} is a sequence j=0 of stationary ALNQD random variables with mean zeros and finite variances.
基金supported by Science and Technology project of the State Grid Corporation of China“Research on Active Development Planning Technology and Comprehensive Benefit Analysis Method for Regional Smart Grid Comprehensive Demonstration Zone”National Natural Science Foundation of China(51607104)
文摘In the process of large-scale,grid-connected wind power operations,it is important to establish an accurate probability distribution model for wind farm fluctuations.In this study,a wind power fluctuation modeling method is proposed based on the method of moving average and adaptive nonparametric kernel density estimation(NPKDE)method.Firstly,the method of moving average is used to reduce the fluctuation of the sampling wind power component,and the probability characteristics of the modeling are then determined based on the NPKDE.Secondly,the model is improved adaptively,and is then solved by using constraint-order optimization.The simulation results show that this method has a better accuracy and applicability compared with the modeling method based on traditional parameter estimation,and solves the local adaptation problem of traditional NPKDE.
基金The project supported by the National Natural Science Foundation of China(50278054)
文摘The polynomial matrix using the block coefficient matrix representation auto-regressive moving average(referred to as the PM-ARMA)model is constructed in this paper for actively controlled multi-degree-of-freedom(MDOF)structures with time-delay through equivalently transforming the preliminary state space realization into the new state space realization.The PM-ARMA model is a more general formulation with respect to the polynomial using the coefficient representation auto-regressive moving average(ARMA)model due to its capability to cope with actively controlled structures with any given structural degrees of freedom and any chosen number of sensors and actuators.(The sensors and actuators are required to maintain the identical number.)under any dimensional stationary stochastic excitation.
基金supported by National Natural Science Foundation of China(61473070,61433004)Fundamental Research Funds for the Central Universities(N130504002)SAPI Fundamental Research Funds(2013ZCX01)
基金Supported by the Academic Funding Projects for Top Talents in Universities of Anhui Province (gxbjZD2022067, gxbjZD2021078)the Key Grant Project for Academic Leaders of Tongling University(2020tlxyxs31, 2020tlxyxs09)。
文摘The m-widely orthant dependent(m-WOD)sequences are very weak dependent random variables.In the paper,the authors investigate the moving average processes,which is generated by m-WOD random variables.By using the tail cut technique and maximum moment inequality of the m-WOD random variables,moment complete convergence and complete convergence of the maximal partial sums for the moving average processes are obtained,the results generalize and improve some corresponding results of the existing literature.
基金National Natural Science Foundation of China (Grant No.60574002)MASCOS grant from Australian Research CouncilNational Natural Science Foundation of China (Grant No.70671018)
文摘The present paper first shows that, without any dependent structure assumptions for a sequence of random variables, the refined results of the complete convergence for the sequence is equivalent to the corresponding complete moment convergence of the sequence. Then this paper investigates the convergence rates and refined convergence rates （or complete moment convergence） for probabilities of moderate deviations of moving average processes. The results in this paper extend and generalize some well-known results.
基金supported by National Natural Science Foundation of China (No. 10571073)
文摘Let {εt;t ∈ Z} be a sequence of m-dependent B-valued random elements with mean zeros and finite second moment. {a3;j ∈ Z} is a sequence of real numbers satisfying ∑j=-∞^∞｜aj｜ 〈 ∞. Define a moving average process Xt = ∑j=-∞^∞aj＋tEj,t ≥ 1, and Sn = ∑t=1^n Xt,n ≥ 1. In this article, by using the weak convergence theorem of { Sn/√ n _〉 1}, we study the precise asymptotics of the complete convergence for the sequence {Xt; t ∈ N}.
基金The National Natural Science Foundation ofChina(No70573068)The Shanghai Education Com-mittee Foundation(No05FZ11)The Shanghai Lead-ing Academic Discipline(NoT0602)
文摘The bullwhip effect in a multistage supply chain was analyzed using sophisticated stationary forecasts (third order moving average and third order exponential smoothing forecasts). The third order exponential smoothing and third order moving average forecasts sometimes have a variance reducing effect on the supply chain.In a supply chain with positively correlated or independent and identically distributed (i.i.d) demands, the order variance based on simple moving average forecast (or simple exponential smoothing forecast) is larger than the order variance based on second order moving average forecast (or second order exponential smoothing forecast),and the order variance based on second order moving average forecast( or second order exponential smoothing forecast) is larger than the order variance based on third order moving average forecast( or third order exponential smoothing forecast). In addition, for i.i.d demands, third order exponential smoothing forecast leads to a larger variation than third order moving average forecast.
基金Research supported by National Natural Science Foundation of China
文摘In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai＋kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞） is an absolutely solutely summable sequence of real numbers.
文摘Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are discussed. We also discuss complete convergence for the moving average processes underB-valued martingale differences assumption.
文摘In this paper we discuss the least-square estimator of the unknown change point in a mean shift for moving-average processes of ALNQD sequence. The consistency and the rate of convergence for the estimated change point are established. The asymptotic distribution for the change point estimator is obtained. The results are also true for ρ-mixing, φ-mixing, α-mixing sequences under suitable conditions. These results extend those of Bai, who studied the mean shift point of a linear process of i.i.d, variables, and the condition ∑j=0^∞j｜aj｜ 〈 ∞ in Bai is weakened to ∑j=0^∞｜aj｜〈∞.
文摘Consistent high-quality and defect-free production is the demand of the day. The product recall not only increases engineering and manufacturing cost but also affects the quality and the reliability of the product in the eye of users. The monitoring and improvement of a manufacturing process are the strength of statistical process control. In this article we propose a process monitoring memory-based scheme for continuous data under the assumption of normality to detect small non-random shift patterns in any manufacturing or service process.The control limits for the proposed scheme are constructed. The in-control and out-of-control average run length(AVL) expressions have been derived for the performance evaluation of the proposed scheme. Robustness to non-normality has been tested after simulation study of the run length distribution of the proposed scheme, and the comparisons with Shewhart and exponentially weighted moving average(EWMA) schemes are presented for various gamma and t-distributions. The proposed scheme is effective and attractive as it has one design parameter which differentiates it from the traditional schemes. Finally, some suggestions and recommendations are made for the future work.
基金The National Natural Science Foundation ofChina(No60504033)
文摘A novel nonlinear combination process monitoring method was proposed based on techniques with memo- ry effect （multivariate exponentially weighted moving average （MEWMA）） and kernel independent component analysis （KICA）. The method was developed for dealing with nonlinear issues and detecting small or moderate drifts in one or more process variables with autocorrelation. MEWMA charts use additional information from the past history of the process for keeping the memory effect of the process behavior trend. KICA is a recently devel- oped statistical technique for revealing hidden, nonlinear statistically independent factors that underlie sets of mea- surements and it is a two-phase algorithm., whitened kernel principal component analysis （KPCA） plus indepen- dent component analysis （ICA）. The application to the fluid catalytic cracking unit （FCCU） simulated process in- dicates that the proposed combined method based on MEWMA and KICA can effectively capture the nonlinear rela- tionship and detect small drifts in process variables. Its performance significantly outperforms monitoring method based on ICA, MEWMA-ICA and KICA, especially for lonu-term performance deterioration.
