Regarch模型的几何遍历性及伴随几何遍历性

本文引入随机环境干扰,将非线性时间序列GARCH模型推广为REGARCH模型,并讨论REGARCH模型的几何遍历性及伴随几何遍历性。     

Hilbert空间中一类新的渐近几乎非扩张曲线的渐近行为与遍历性

引入了Ｈｉｌｂｅｒｔ空间中一类新的渐近几乎非扩张曲线，并讨论了这类新的渐近几乎非扩张曲线的渐近行为与遍历性，进一步，作为应用，得到了Ｈｉｌｂｅｒｔ空间中非Ｌｉｐｓｃｈｉｔｚ映象的非线性算子族的渐近行为与遍历性方面的结果。     

宽平稳序列均方遍历性的两个充要条件(英文)

本文研究了宽平稳序列具有均方遍历性的充要条件问题.利用施瓦兹不等式,获得了复宽平稳序列均方遍历性的两个充要条件和一个易于验证的充分条件.     

复平稳随机序列均值遍历性的两个充要条件

遍历性是平稳随机过程的一个核心问题,在实践中有重要的应用.这里首先给出复平稳序列均值遍历性的一个等价定义,在此基础上证明了复平稳序列情形下均值遍历性的两个充要条件,并给出一个形式简单的推论,这些结果有助于深入的理解复平稳过程的均值遍历性,同时也为估计复平稳过程的均值提供了一种简单高效的方法.     

带拯救的广义非线性Markov分枝模型的稳定性

该文考虑了一类带拯救的广义非线性Markov分枝模型.首先讨论了带拯救的广义非线性Markov分枝q-矩阵发生函数的性质,通过发生函数给出了过程的正则性和唯一性判别准则,得到了没有拯救情形下过程的灭绝概率和平均灭绝时间,并讨论了带有拯救情形下模型的稳定性和遍历性,得到了过程的常返性和遍历性的充分必要条件.最后,给出了遍历情形下该过程的平稳分布.     

一般状态空间跳过程的强遍历性

研究了一般状态空间跳过程的强遍历性,利用最小非负解理论及马氏性,得到了强遍历性的几个等价条件,把连续时间可数状态马氏链的相关结果推广到一般状态空间跳过程的情形.     

一般形式的连续时间拟生灭过程各种遍历性判定准则

侯振挺、李晓花在 [1]已经讨论了具有某些特殊形式的拟生灭过程各种遍历性 ,我们将在此基础讨论一般形式连续时间拟生灭过程各种遍历性 ,并给出 [1]中连续时间拟生灭过程的指数遍历及多项式遍历的一个新证明 ,该证明给出了具有某些特殊条件下连续时间拟生灭过程遍历性与离散时间拟生灭过程遍历性之间关系 .     

基于等时圆矢量差分的ARVMA组合模型及其实证研究

对于非平稳的时间序列,直接差分会丢失很多有价值的信息,增大建模误差.采用与传统的数学改进方法不同的物理模型,对非平稳时间序列提出了基于矢量差分的ARVMA(Autoregressive Vectorized Moving Average Model)组合模型.借助矢量三角形非线性的可加性以及等时圆中质点沿弦下滑的等时性,构建等时圆中的矢量差分方法和由点出发的时间序列,并用作用力函数的极大值阐释了最大价格的产生机制.然后,利用矢量差分可以减弱过度差分的优良性及差分时一阶自相关系数的自适应性,充分论证了非线性的矢量差分在消除非平稳趋势时可以最大程度地保留原始数据的信息量.最后,对IBM股票日收盘价数据进行实证研究.实证结果表明:等时圆矢量差分方法与直接差分相比预测误差更小.     

关于可列非齐次马氏链的广义C-强遍历性

马氏链遍历性理论在生物,数值计算,信息理论,自动控制,近代物理和公用事业中的服务系统等众多领域都有着广泛的应用,马氏链的C-强遍历性是马氏链遍历性理论的重要内容.本文给出了马氏链C-强遍历性的一个推广,首先给出了在可列状态空间取值的非齐次马氏链的广义C-强遍历性和广义一致C-强遍历性的概念,然后研究这两种遍历性成立的充分条件.     

Grid-Search和PSO优化的SVM在Shibor回归预测中的应用研究

作为一种动态和非稳定时间序列,Shibor发展变化是随机波动的,难以准确预测Shibor的波动性.支持向量机(SVM)在回归预测非线性时间序列方面有很好地预测效果,SVM的预测精度和泛化能力的核心是参数的优化选择,分别用网格搜索法(Grid-Search)和粒子群(PSO)算法来优化SVM的参数c和g.从而将参数优化后的SVM非线性回归预测法与基于传统ARIMA时间序列预测结果进行对比分析.实验表明,优化后的SVM回归预测方法比ARIMA时间序列方法更精确,在实际中具有很大的应用价值.     

Linear independence of root equations forM/G/1 type Markov chains

There is a classical technique for determining the equilibrium probabilities ofM/G/1 type Markov chains. After transforming the equilibrium balance equations of the chain, one obtains an equivalent system of equations in analytic functions to be solved. This method requires finding all singularities of a given matrix function in the unit disk and then using them to obtain a set of linear equations in the finite number of unknown boundary probabilities. The remaining probabilities and other measures of interest are then computed from the boundary probabilities. Under certain technical assumptions, the linear independence of the resulting equations is established by a direct argument involving only elementary results from matrix theory and complex analysis. Simple conditions for the ergodicity and nonergodicity of the chain are also given.     

Detection of multiple change-points in multivariate time series

We consider the multiple change-point problem for multivariate time series, including strongly dependent processes, with an unknown number of change-points. We assume that the covariance structure of the series changes abruptly at some unknown common change-point times. The proposed adaptive method is able to detect changes in multivariate i.i.d., weakly and strongly dependent series. This adaptive method outperforms the Schwarz criteria, mainly for the case of weakly dependent data. We consider applications to multivariate series of daily stock indices returns and series generated by an artificial financial market. __________ Translated from Lietuvos Matematikos Rinkinys, Vol. 46, No. 3, pp. 351–376, July–September, 2006.     

C_0复杂度的改进及其在证券市场中的应用

系统地分析了Lemple-Ziv复杂性度量方法的应用过程中,将实际信号(时间序列)转变成符号序列的诸多方法中存在的一些问题,提出了更合理兼容法.该方法可以有效地刻划各种时间序列的复杂度.文章最后动态地分析了中国证券市场的复杂性.     

基于随机截尾数据的指数型元件串联系统可靠性的置信限

基于元件的随机定时截尾寿命试验数据 ,给出了指数型元件串联系统可靠性的经典精确置信下限 ,给出了数字例 .     

Weighted norms in subspace‐based methods for time series analysis

Many modern approaches of time series analysis belong to the class of methods based on approximating high‐dimensional spaces by low‐dimensional subspaces. A typical method would embed a given time series into a structured matrix and find a low‐dimensional approximation to this structured matrix. The purpose of this paper is twofold: (i) to establish a correspondence between a class of SVD‐compatible matrix norms on the space of Hankel matrices and weighted vector norms (and provide methods to construct this correspondence) and (ii) to motivate the importance of this for problems in time series analysis. Examples are provided to demonstrate the merits of judiciously selecting weights on imputing missing data and forecasting in time series. Copyright © 2016 John Wiley & Sons, Ltd.     

Central limit theorems for arrays of decimated linear processes

Linear processes are defined as a discrete-time convolution between a kernel and an infinite sequence of i.i.d. random variables. We modify this convolution by introducing decimation, that is, by stretching time accordingly. We then establish central limit theorems for arrays of squares of such decimated processes. These theorems are used to obtain the asymptotic behavior of estimators of the spectral density at specific frequencies. Another application, treated elsewhere, concerns the estimation of the long-memory parameter in time series, using wavelets.     

Wavelet variance analysis for gappy time series

The wavelet variance is a scale-based decomposition of the process variance for a time series and has been used to analyze, for example, time deviations in atomic clocks, variations in soil properties in agricultural plots, accumulation of snow fields in the polar regions and marine atmospheric boundary layer turbulence. We propose two new unbiased estimators of the wavelet variance when the observed time series is ‘gappy,’ i.e., is sampled at regular intervals, but certain observations are missing. We deduce the large sample properties of these estimators and discuss methods for determining an approximate confidence interval for the wavelet variance. We apply our proposed methodology to series of gappy observations related to atmospheric pressure data and Nile River minima.     

下三角双线性时间序列模型的近似三阶矩结构和双谱密度

下三角双线性时间序列模型，特别是它的一些简单的特殊情况，被许多人研究过。但对于一般形式，目前，只知道其二阶结构(自协方差和谱)与线性ARMA模型相似.而反映该模型特征的三阶结构(三阶矩和双谱),由于既繁琐又复杂而很难获得(文献中尚未见报道）。该文给出一种计算三阶矩和双谱的 近似方法。特别地，对于可分离的下三角双线性时间序列模型，得到了比较简洁实用的计算公式。     

On joint identification of the feedback parameters for hyperchaotic systems: An optimization-based approach

We propose an optimization-based scheme for parameter estimation in high-dimensional chaotic systems, and the symbolic time series analysis (STSA) based method is adopted to address the estimation problem. It is shown that, when the system structure and the corresponding time series are known, the STSA-based method works better with respect to the autocorrelation function (ACF) and the mutual information (MI) technologies. Most importantly, the time delay and the feedback strength of two test systems, i.e., the Mackey–Glass system and an external-cavity semiconductor laser system, can be successfully identified using the proposed scheme. To explore the noise immunity, the influence of certain levels of noise on the STSA-based method is tested.     

Time series analysis for ground penetrating radar (GPR) asphalt thickness profile

Time series obtained from the waveform profiles of the ground penetrating radar (GPR) thickness of the asphaltic concrete layers of in–service pavement holds a key to the understanding of thickness variation and the presence of cavities within and below the pavement surface. In this paper, the fundamental techniques of time series modelling—(i) identification, (ii) estimation and (iii) diagnostics—are applied to the GPR thickness profile of three types of pavement—(a) fully–designed (b) partially–designed and (c) compositely designed pavement. Actual applications are made using data from in–service pavement in the state of Kansas. The main purpose of this study is to investigate the mechanism that drives the data and to compare the model errors and statistics of the thickness profiles of different types of flexible pavement. In the present study, the time series is replaced by a distance scale, but the name time series is retained.