时间序列系统建模预测的一种新方法

利用微分方程数值解法对时间序列系统建模作了新的探讨 ,给出了单调型和起伏型时间序列的建模预测方法 .本文给出的方法适用范围广泛 ,尤其对间隔较小的时间序列能获得满意的精度 ,文中最后给以建模实例 .     

Computation of the Chebyshev-Padé table

A recursive method is given for the computation of the coefficients in the Chebyshev-Padé table. This is a table, recently defined by Clenshaw and Lord for Chebyshev series, which is analogous to the Padé table for power series. The method enables one to compute the whole of the triangular part of the table which derives from the given number of terms in the original Chebyshev series taken into account. The recursive method given by Clenshaw and Lord only enables one to compute the coefficients in half of this table.     

一种改进的基于指数平滑神经网络模型的时间序列预测方法

基于指数平滑模型与误差反传神经网络法提出了一个改进的时间序列预测方法.将神经网络模型移植入指数加权滑动平均模型中,充分考虑了时间序列的部分线性性和非线性性对预测结果的影响,是传统的混合模型的一个更合理的改进.最后通过对上证指数时间序列的实证分析,以预测均方误差为检验标准,对五种常用的时间序列预测模型进行了预测精度的比较,而且经验证所提出的改进的时间序列预测模型相对来说具有更小的预测均方误差.     

二项式系数倒数级数恒等式

利用已知级数,通过裂项构造出一批新的二项式系数倒数级数,它们的分母分别含有1到4个奇因子与二项式系数的乘积表达式.所给出二项式系数倒数级数的和式是封闭形的.     

Usage of the homotopy analysis method for solving the nonlinear and linear integral equations of the second kind

The paper presents an application of the homotopy analysis method for solving the nonlinear and linear integral equations of the second kind. In this method a series is created, sum of which (if the series is convergent) gives the solution of discussed equation. Conditions ensuring convergence of this series are presented in the paper. Error of approximate solution, obtained by considering only partial sum of the series, is also estimated. Examples illustrating usage of the investigated method are presented as well, including the example having practical application for calculating the charge in supply circuit of flash lamps used in cameras.     

基于主成分分析的单变量时间序列聚类方法

针对时间序列数据的高维特性,在进行理论分析的基础上,利用主成分分析法提出了一种单变量时间序列数据降维的新方法,进而提出了基于主成分分析的单变量时间序列聚类方法。其主要思想是在线性空间中的同一组基下,用系数之间的相似性来刻画对应时间序列之间相似性,在理论分析过程中,首先对单变量时间序列数据集进行主成分分析,其次分析了单变量时间序列数据集、样本协方差矩阵的特征向量与主成分之间的关系,并证明了由主成分构成的向量组线性无关。为了进一步验证理论分析结果的正确性和所提算法的有效性,分别利用仿真数据和真实的股票数据进行了数值实验。     

Book review

Hypergeometric series identities are revisited systematically by means of Abel's method on summation by parts. Several new formulae and transformations are also established. The author is convinced that Abel's method on summation by parts is a natural choice in dealing with classical hypergeometric series.     

基于小波变换和改进萤火虫算法优化极限学习机的短期负荷预测

提出了一种基于小波变换和改进萤火虫优化极限学习机的短期负荷预测方法.通过小波分解和重构,对原始负荷序列进行降噪;在模型训练阶段利用改进的萤火虫算法优化极限学习机参数,获得各序列的最优模型;针对各子序列分别预测叠加得到最终预测值.通过在两种时间尺度的数据序列上进行数值计算,与传统的ARMA、BP神经网络、支持向量机及LSSVM等多种经典预测模型相比,模型预测效果更优.     

Controlling based method for modelling chaotic dynamical systems from time series

A simple method is introduced for modelling chaotic dynamical systems from the time series, based on the concept of controlling of chaos by constant bias. In this method, a modified system is constructed by including some constants (controlling constants) into the given (original) system. The system parameters and the controlling constants are determined by solving a set of implicit nonlinear simultaneous algebraic equations which is obtained from the relation connecting original and modified systems. The method is also extended to find the form of the evolution equation of the system itself. The important advantage of the method is that it needs only a minimal number of time series data and is applicable to dynamical systems of any dimension. It also works extremely well even in the presence of noise in the time series. The method is illustrated in some specific systems of both discrete and continuous cases.     

Mining time series data for segmentation by using Ant Colony Optimization

In trying to distinguish data features within time series data for specific time intervals, time series segmentation technology is often required. This research divides time series data into segments of varying lengths. A time series segmentation algorithm based on the Ant Colony Optimization (ACO) algorithm is proposed to exhibit the changeability of the time series data. In order to verify the effect of the proposed algorithm, we experiment with the Bottom-Up method, which has been reported in available literature to give good results for time series segmentation. Simulation data and genuine stock price data are also used in some of our experiments. The research result shows that time series segmentation run by the ACO algorithm not only automatically identifies the number of segments, but its segmentation cost was lower than that of the time series segmentation using the Bottom-Up method. More importantly, during the ACO algorithm process, the degree of data loss is also less compared to that of the Bottom-Up method.     

A study of the convergence of and error estimation for the homotopy perturbation method for the Volterra–Fredholm integral equations

In this work the solution of the Volterra–Fredholm integral equations of the second kind is presented. The proposed method is based on the homotopy perturbation method, which consists in constructing the series whose sum is the solution of the problem considered. The problem of the convergence of the series constructed is formulated and a proof of the formulation is given in the work. Additionally, the estimation of the approximate solution errors obtained by taking the partial sums of the series is elaborated on.     

Measurement‐error detection: international evidence on industrial production

The existence or non‐existence of measurement error (ME) in observed time series is examined not by hypothesis testing but by model selection using the values of information criteria of a battery of alternative models with and without ME. Whether the time series contains ME is determined as a result of model selection. This method is compared with recently proposed hypothesis‐testing method. Simulation results suggest that the performances of the proposed method are usually comparable to and sometimes better than those of the hypothesis‐testing method. The proposed method is applied to monthly time series of industrial production for fifteen developed countries. Obtained results indicate that MEs are detected for at least one and at most seven countries. Copyright © 2006 John Wiley & Sons, Ltd.     

求函数项级数收敛区间的一种新方法

对形如∑∞n=0anxkn+b(k∈,b∈)的幂级数,当其缺项的时候,不能直接用公式ρ=li mn→∞an+1an求其收敛半径与收敛区间(本文约定收敛区间不含端点),一般都是直接采用达朗贝尔(比值)判别法求其收敛半径与收敛区间.事实上,对这种幂级数只需先作一个变量代换,就可以采用公式法求解.本文给出了这种方法的理论证明,并将结论进行了推广,即利用变量代换与公式法同样可求形如∑∞anxkn+bs(k,s∈,b∈)形式的函数项级数的收敛区间.     

Approximate solutions for time-fractional two-component evolutionary system of order $2$ using coupled fractional reduced differential transform method

In this paper, Coupled Fractional Reduced Differential Transform method is extended to apply to the generalized time-fractional two-component evolutionary system of order 2. By using this method, the solutions in the form of a generalized Taylor series are obtained. The graphics of numerical solutions together with the error analysis demonstrate that the present method is effective and accurate for obtaining approximate solutions of fractional coupled equations. Moreover, the results also indicate that the solutions obtained by residual power series method in previous literature (M. Alquran, Analytical solution of time-fractional two-component evolutionary system of order 2 by residual power series method, J. Appl. Anal. Comput.,5(2015)(4), 589-599.) contain errors.     

基于傅里叶分析法的股票市场超高频数据相关性分析

股票市场超高频数据具有交易间隔随机性的特点,传统的皮尔逊相关性度量不能够直接使用原始交易数据,需要通过插值得到均匀、同步的抽样序列.傅里叶分析法不需要对原始数据进行插值,能更精确地度量时间序列的相关性.将傅里叶分析法用于我国金融市场股票收益率的相关性分析中,对皮尔逊相关分析和傅里叶分析法的度量效果进行了比较.     

求解准确的表面张力—重力波方程的新方法

本文提供一个求解重力和表面张力同时作用的周期前进二维非线性波的新方法.自由表面在计算域转入单位圆后用有限项Fourier级数表示.动力学边界条件用的是完整的非线性形式.Fourier级数的系数用Newton-Raphson方法迭代求解.这是一个精巧的方法.所用计算工作量小而结果精度高.     

时间序列分解预测法及周期因素的探讨

本文运用时间序列分解预测法，分析门诊人次的变动规律，预测了季度门诊人次。本法与移动平均比率预测法相比，预测精度提高３１％。本文还探讨了时间序列分解预测的周期因素等有关问题。     

Stock market forecasting by using a hybrid model of exponential fuzzy time series

The initial aim of this study is to propose a hybrid method based on exponential fuzzy time series and learning automata based optimization for stock market forecasting. For doing so, a two-phase approach is introduced. In the first phase, the optimal lengths of intervals are obtained by applying a conventional fuzzy time series together with learning automata swarm intelligence algorithm to tune the length of intervals properly. Subsequently, the obtained optimal lengths are applied to generate a new fuzzy time series, proposed in this study, named exponential fuzzy time series. In this final phase, due to the nature of exponential fuzzy time series, another round of optimization is required to estimate certain method parameters. Finally, this model is used for future forecasts. In order to validate the proposed hybrid method, forty-six case studies from five stock index databases are employed and the findings are compared with well-known fuzzy time series models and classic methods for time series. The proposed model has outperformed its counterparts in terms of accuracy.     

基于复傅里叶级数展开的最低身故利益保障寿险产品的定价

本文利用复傅里叶级数展开方法(CFS)对最低身故利益保障(GMDB)寿险产品进行定价,其主要的思想是对辅助函数进行傅里叶级数展开.本文考虑了两种剩余寿命密度函数的形式,即联合指数形式和分段常数死亡率形式,并通过运用已知的Levy模型的特征函数来估计级数的系数.我们将主要考虑看涨期权和看跌期权下GMDB产品的定价问题,在数值实验部分我们还通过与余弦级数展开方法(COS)和蒙特卡洛方法(MC)进行比较来说明CFS在计算精度和运行时间方面的优势.     

常微分方程的级数解法探源

级数法是求解常微分方程最有效的方法之一.牛顿是第一位真正开始求解微分方程的数学家,级数法是其采用的第一种求解方法.在研读牛顿的微积分论文《流数法与无穷级数》基础上,探讨级数法形成的根源,揭示其思想方法对今日微分方程课程教与学的启迪作用以及对创立和发展微分方程学科的重要理论意义.