SPECTRAL RADIUS,KRONECKER PRODUCTS AND STATIONARITY

Abstract. We provide a stochastic proof of the inequality ρ(A?A+B?B) ≥ρ(A?A), where ρ(M) denotes the spectral radius of any square matrix M, i.e. max{|eigenvalues| of M}, and M?N denotes the Kronecker product of any two matrices M and N. The inequality is then used to show that stationarity of the bilinear model will imply stationarity of the linear part, i.e. the linear ARMA model for r= 1 and q= 1. Furthermore, it is shown that stationarity of the subdiagonal model, i.e. the bilinear model with b_ij=0 for i< j, again implies stationarity of its linear part, provided that the stationarity condition given by Bhaskara Rao and his colleagues is met. Interestingly, the conclusion that stationarity of the subdiagonal models, implies that the linear component models cannot be extended to the general non-subdiagonal bilinear models. The last observation is demonstrated via a simple example with p=m= 1, r= 0 and q= 2.     

Time Dependence and Moments of a Family of Time-Varying Parameter Garch in Mean Models

Abstract.  In this paper we consider the time series dependence, stationarity, and higher moments issues of a family of first-order conditionally heteroskedastic in mean models with a possibly time-varying mean parameter. The interest in these models lies in the fact that economic theory and physics often require the connection between the first and second conditional moments of time series. Our results reveal important properties of these models, which are consistent with stylized facts in financial and turbulence data sets. They can also be employed for model identification, estimation, and testing.     

ON THE EXISTENCE OF STATIONARY THRESHOLD AUTOREGRESSIVE MOVING-AVERAGE PROCESSES

Abstract. Conditions for the existence of causal and strictly stationary solutions of the equations defining a self-exciting threshold autoregressive moving-average (SETARMA) model are derived. For threshold autoregressive models we allow the autoregressive coefficients to be random and derive sufficient conditions for geometric ergodicity and the existence of strictly and weakly stationary solutions of the defining equations.     

基于车体横移振动的高速列车虚拟复合阻尼天棚控制算法研究

高速列车车体横向随机振动由车体的横移振动、侧滚振动和摇头振动三自由度合成,是影响车体横向运行平稳性的关键;为了改善列车横向运行平稳性,提高半主动控制性能;通过建立某型高速列车动力学模型,对车体横向振动特性进行分析,得出横移振动的加剧是造成车体合成横向振动和横向平稳性恶化的主要原因;通过分析在传统天棚阻尼控制算法下分别以车体合成横向振动为反馈和以横移振动为反馈对车体横向振动的控制效果,得出采用以车体横移振动为反馈的传统天棚阻尼控制算法对车体横向振动的抑制效果更佳;在此基础上,提出一种以车体横移振动为反馈的虚拟复合阻尼天棚控制算法,并进行联合仿真分析;结果表明:相比于被动控制,采用虚拟复合阻尼天棚控制算法后,车体合成横向振动加速度峰值、均方根值和平稳性改善率分别达到了46%、43%和19.5%,均高于采用传统天棚阻尼控制算法;可见,采用虚拟复合阻尼天棚控制算法在抑制车体合成横向振动,改善车体横向平稳性方面控制性能更佳。     

高速列车多目标约束横向半主动控制算法研究

传统的高速列车横向半主动控制研究,主要以提高车体横向运行平稳性为目的;但车体与各部件之间通过二系悬挂与一系悬挂连接传递相互耦合振动作用,因此半主动控制在改善车体横向平稳性的同时,将导致构架横向振动和轮轨横向作用加剧,从而使得列车脱轨系数增大,列车运行安全性能变差;针对这一问题,提出在虚拟惯性阻尼半主动控制和脱轨安全半主动控制的基础上,设计两个控制回路的多目标约束下的混合半主动控制算法,在实现列车横向半主动控制提高平稳性的同时,控制脱轨系数的恶化,从而同时提高列车平稳性和脱轨安全性能;并利用Simpack建立了某型高速列车多刚体动力学模型,联合Matlab/Simulink建立了联合仿真分析系统对车体横向半主动控制进行研究;结果表明:采用多目标约束半主动控制算法后,车体横向振动加速度峰值和均方根值分别降低了36%和34%,平稳性改善了15%,脱轨系数减小了17%;可见采用多目标约束半主动控制算法不仅能够有效抑制车体横向振动,改善列车运行平稳性,而且还能减小列车脱轨系数,提高列车运行安全性。     

一种图像序列平稳性和相关性检验的天气场景分类方法

提出一种利用图像序列的平稳性和相关性检验的天气场景分类方法.首先,给出天气场景的定义和分类标准;其次,该方法通过分段逆序平稳性检验,提出图像均值子序列逆序总数数学期望和方差的计算方法,将天气场景分为平稳性天气场景和非平稳性天气场景;最后,提出自相关函数的分类检验方法,建立对待分类场景图像序列的激变描述,完成对其所属静态...     

非平稳信号度量方法综述

非平稳性度量是非平稳信号处理中的重要课题。尽管已有的度量方法在原理上有较大差异,缺少统一的理论框架和度量标准,但这些非平稳信号度量方法都在其相应领域发挥了重要作用。本文对随机信号非平稳度量方法进行了综述,系统地总结、归纳了不同领域现有的随机信号非平稳性度量方法,包括基于统计量和动力学参数的时域方法、时频域参数方法、信号建模参数方法以及特定类别信号的非平稳性度量方法,给出了各种度量方法的应用,并展望了非平稳性度量的未来发展方向。     

土性剖面随机场模型的平稳性和各态历经性验证

本文根据平稳的和各态历经的随机过程的基本概念及大量钻孔资料，提出了静力触探数据空间分布的平稳性和各态历经性检验的必要性及检验方法；讨论了相关函数形式的选择；通过大量计算比较了求解相关距离的各种方法；分析了相关距离这个概念的工程应用。     

Quasi-maximum likelihood estimation of periodic GARCH and periodic ARMA-GARCH processes

Abstract.  This article establishes the strong consistency and asymptotic normality (CAN) of the quasi-maximum likelihood estimator (QMLE) for generalized autoregressive conditionally heteroscedastic (GARCH) and autoregressive moving-average (ARMA)-GARCH processes with periodically time-varying parameters. We first give a necessary and sufficient condition for the existence of a strictly periodically stationary solution of the periodic GARCH (PGARCH) equation. As a result, it is shown that the moment of some positive order of the PGARCH solution is finite, under which we prove the strong consistency and asymptotic normality of the QMLE for a PGARCH process without any condition on its moments and for a periodic ARMA-GARCH (PARMA-PGARCH) under mild conditions.