近似周期时间序列分析（英文）

本文首先给出了近似周期时间序列概念,即:具有周期特征但是周期长度变化的时间序列.比如,太阳黑子序列具有11年左右的周期,但是其周期并不是11,而是在11左右变化,这就是一个近似周期序列.然后给出了提取近似周期趋势方法,并且提出了广义差分算子,这里提出的广义差分算子不仅可以消除时间序列的长期趋势和周期性,而且还可以消除近似周期性.最后,以太阳黑子序列为例说明了广义差分算子的应用.     

具有周期特征的离散时间序列的非参数可加模型

周期性是在时间序列分析中经常出现的影响因素之一.在离散值响应变量时间序列中,我们利用带惩罚的极大似然估计建立了未知周期的一致估计.基于周期的估计,我们利用B-样条逼近趋势项和可加函数,同时得到了周期项的√n相合估计以及趋势项和可加函数的初始估计.然后基于后移的思想,推导了趋势项和可加函数的改进估计,并证明了估计量的渐近...     

存在趋势和周期特征的非平稳时间序列的建模及其应用

本文研究存在未知周期和趋势的非平稳时间序列的估计问题.将经典的时间序列分解模型写成一个含有未知参数的部分线性模型,首先采用B-样条逼近未知时间趋势,然后利用惩罚最小二乘回归法得到未知周期、周期序列和趋势的估计.本文还给出估计量的理论性质,包括周期估计的相合性以及周期序列和趋势估计的渐近性质.模拟研究展现了本文方法的优越...     

变系数的周期性时间序列模型及其应用

存在于各个领域的时间序列不仅表现出周期性的特征还易受外界因素的影响,而且外界因素的影响并非一成不变,同时,部分时间序列的周期是未知的.对于这样的易受外界因素影响的周期性时间序列,本文旨在构造含有变系数函数的周期性序列模型.将经典的时间序列模型分解成一个含有未知参数的部分线性变系数模型,利用B样条逼近外生变量的变系数函数,借助带有l₀惩罚项的最小二乘回归得到未知周期、周期序列以及外生变量的影响系数的估计结果.本文还给出了估计量的理论性质,包括周期估计的相合性、周期序列估计和变系数函数估计的渐近性质.通过第4章的模拟,我们展现了本文方法的优越性.最后我们通过三个实际数据的应用展现了本文方法的实用性.     

一类广义耦合的非线性波动方程组时间周期解的存在性

研究了一类广义耦合的非线性波动方程组关于时间周期解的问题.首先利用Galerkin方法构造近似时间周期解序列,然后利用先验估计和Laray-Schauder不动点原理,证明近似时间周期解序列的收敛性,从而得到该问题时间周期解的存在性.     

一类KdV非线性Schr(o)dinger组合微分方程组时间周期解的存在性

本文研究了一类KdV非线性Schr(o)dinger组合微分方程组时间周期解的问题,首先利用Galerkin方法构造近似时间周期解序列,然后利用先验估计和Leray-Schauder不动点原理,证明近似时间周期解序列的收敛性,从而得到该问题时间周期解的存在性.     

线性递归序列模q

设{uk}k≥0为一个线性递归序列.序列{uk(mod q)}k≥0是周期的,很多人都对其周期有过研究.本文应用二次数域中理想的理论,较完全地刻画了二次线性递归序列模q的周期长度,所获结果加强并推广了Engstrom及Wall的结论.     

周期相关时间序列与周期自回归模型

介绍了周期相关时间序列和周期自回归模型,并研究了周期自回归时间序列的稳定性及周期性,得到了它为周期相关时间序列的一个充要条件,推广了文献[1]的结论.     

用SASD统计包预报含季节变化数据

一、引言 时间序列分析可以揭示一个按时间间隔搜集的统计资料所反映的规律.一直掌握这种规律,即可对未来作出估计,这种估计就是预报.预报是任何决策的基本工具,它对 工程技术人员和管理人员是非常重要的。 时间序列中通常包括四种变化成分;长期趋势、周期波动、季节变动和随机变化.长期趋势是指变量值在一个长期内所呈现的增加或减小的趋势.周期波动是指在一年以上的时期内,时间序列沿其长期趋势线上摆动的波动变化.季节变动是指在一年内围绕趋势线的可以预报的重复运动.随机变化是指时间序列中的随机变化因素. 随机数据统计分析软件包SA…     

q元m序列非周期自相关函数的估计与M序列的分段线性化

序列的非周期自相关函数的估计,具有良好非周期自相关性的序列的构造,以及非线性M序列的相关性等方面已有的成果较少.著名的Barker序列当长度大于13时是否存在的问题尚未完全解决,L序列的非周期自相关函数的估计仅在长度较短时有一些数值计算结果,文献曾估计了一类二元序列非周期自相关函数的上界.最近,章照止巧妙地应用组合数学方法估计了状态两两不同的二元序列中一元的个数(在这基础     

A perturbation treatment for optimal slightly nonlinear systems with linear control and quadratic criteria

Recently, it has been discovered that symbolic algebraic manipulations can be performed on the computer with input/output data in symbolic form. Accordingly, and for slightly nonlinear two-point boundary-value problems, it is feasible to obtain approximate analytical solutions in the form of power series in a small parameter. In these solutions, the boundary values are presented in a literal form. In this paper, the Lie canonical transformation is applied to derive approximate optimal solutions for slightly nonlinear systems with quadratic criteria. The transformation generator is determined by simple partial differential equations of the first order. To determine the arbitrary constants of the transformation in terms of the two-point boundary values, inversion of a vectorial power series in a small parameter is required, and a recursive algorithm for this inversion is given. To express the final solution in terms of these boundary values, a substitution of the inverted vectorial power series into another vectorial power series is also necessary, and a recursive algorithm for this substitution is presented.The authors are indebted to Professor J. V. Breakwell for his suggestions.     

Determination of periodic orbits of nonlinear oscillators by means of piecewise-linearization methods

An approximate method based on piecewise linearization is developed for the determination of periodic orbits of nonlinear oscillators. The method is based on Taylor series expansions, provides piecewise analytical solutions in three-point intervals which are continuous everywhere and explicit three-point difference equations which are P-stable and have an infinite interval of periodicity. It is shown that the method presented here reduces to the well-known Störmer technique, is second-order accurate, and yields, upon applying Taylor series expansion and a Padé approximation, another P-stable technique whenever the Jacobian is different from zero. The method is generalized for single degree-of-freedom problems that contain the velocity, and (approximate) analytical solutions are presented. Finally, by introducing the inverse of a vector and the vector product and quotient, and using Taylor series expansions and a Padé approximation, the method has been generalized to multiple degree-of-freedom problems and results in explicit three-point finite difference equations which only involve vector multiplications.     

小波分析方法在金融股票数据预测中的应用

利用小波分析预测方法对金融数据—股票收盘价这一典型的非平稳时间序列进行预测.使用M a llat小波分解算法对数据进行分解,对分解后的数据进行平滑处理,然后再进行重构,而重构之后的数据就成为近似意义的平稳时间序列,这样就得到了原始数据的近似信号,再应用传统时间序列预测方法对重构后的数据进行预测,将预测结果与实际值,以及和传统预测方法预测结果比较,小波分析方法预测效果更为理想.     

A reliable aftertreatment for improving the differential transformation method and its application to nonlinear oscillators with fractional nonlinearities

A new aftertreatment technique is developed in this paper to deal with the truncated series derived by the differential transformation method (DTM) to obtain approximate periodic solutions. The proposed aftertreatment technique splits into two types, named as (Sine-AT technique, SAT) and (Cosine-AT technique, CAT). It is shown that the differential transformation method with the proposed aftertreatment technique is very effective and convenient for a class of nonlinear oscillatory problems with fractional nonlinearities without any need for Padé approximants or Laplace transform.     

Symmetric patterns in the Dirichlet problem for a two-cell cubic autocatalytor reaction model

By using an approach developed by one of the authors, approximate solutions of the soft periodic boundary conditions for a two-cell reaction diffusion model have been obtained. The system is considered with reactant A and autocatalyst B. The reaction is taken cubic in the autocatalyst in the two-cell with linear exchange through A. The formal exact solution is obtained which is symmetric with respect to the mid-point of the container. Approximate solutions are found through the Picard iterative sequence of solutions constructed after the exact one. It is found that the solution obtained is not unique. When the initial conditions are periodic, the most dominant modes initiate to traveling waves in systems with moderate size. Symmetric configurations forming a parabolic one for large time are observed. In systems of large size, spatially symmetric chaos are produced which are stationary in time. Furthermore, it is found the symmetric pattern formation hold irrespective of the condition of linear instability against small spatial disturbance.     

n维欧氏空间的等角变换

在文[1—4]的基础上,运用矩阵理论讨论了”维欧氏空间上的等角变换的判定条件和性质以及可对角化的几个必要条件,对现有结论有一定的推广．     

Decomposition method for the Camassa–Holm equation

The Adomian decomposition method is applied to the Camassa–Holm equation. Approximate solutions are obtained for three smooth initial values. These solutions are weak solutions with some peaks. We plot those approximate solutions and find that they are very similar to the peaked soliton solutions. Also, one single and two anti-peakon approximate solutions are presented. Compared with the existing method, our procedure just works with the polynomial and algebraic computations for the CH equation.     

Estimating long-range dependence in the presence of periodicity: An empirical study

Recent results in applied statistics have shown that the presence of periodicity in a time series may have an influence on the estimation of the long memory (long-range dependence) parameter H. In particular, some estimators falsely detect the presence of long-range dependence when periodicity is present. In this paper, we apply various estimation procedures to synthetic periodic time series in order to verify the performance of each estimation method and to determine which estimators should be used when periodicity may be present.