非线性时间序列建模的异方差混合双AR模型

研究了可用于非线性时间序列建模的异方差混合双自回归模型(heteroscedastic mixture double- autoregressive model,HMDAR),给出了HMDAR模型的平稳性条件,利用ECM(expectation conditional maximization)算法来估计模型的参数,运用BIC(Bayes information criterion)准则来选择模型．HMDAR模型条件分布富于变化的特征使它能够对具有非对称或多峰分布的序列进行建模,将HMDAR模型应用于几个模拟和实际数据集均得到了较为满意的结果,特别是对波动较大的序列,HMDAR模型能比其他模型更好地捕捉到数据序列的特征．     

非线性时间序列建模的混合自回归滑动平均模型

提出了一类用于非线性时间序列建模的混合自回归滑动平均模型(MARMA).该模型是由K个平稳或非平稳的ARMA分量经过混合得到的.讨论了MARMA模型的平稳性条件和自相关函数.给出了MARMA模型参数估计的期望极大化(expectation maximization)算法.运用贝叶斯信息准则(Bayes information criterion)来选择该模型.MARMA模型分布形式富于变化的特征使得它能够对具有多峰分布以及条件异方差的序列进行建模.通过两个实例验证了该模型,并和其他模型进行比较,结果表明MARMA模型能够更好地描述这些数据的特征.     

一类非线性周期时间序列模型

为了描述周期时间序列中的偏倚和多峰等非线性特征,结合有限混合模型方法,提出混合周期自回归滑动平均时间序列模型（MPARMA）,给出了MPARMA模型的平稳性条件,讨论了期望最大化（EM）算法的应用,通过PM10浓度序列分析,评估了MPARMA模型的表现。     

GARCH非线性时间序列模型的网络流量预测

网络流量预测在拥塞控制、网络管理与诊断、路由器设计等领域都具有重要意义。根据当今网络流量的特点,传统的ARMA模型在描述网络流量数据特性时有一定的局限性,从而影响网络流量预测的精度。针对这个问题,研究了使用广义自回归条件异方差模型(GARCH)对网络流量数据进行建模的方法,通过仿真实验表明,该模型可以较好地描述网络流量数据的异方差性,同时其预测精度较之传统的ARMA模型的预测精度也得到了大幅提升。     

基于异方差高斯过程的时间序列数据离群点检测

时间序列数据在测量过程中通常受到事物内在可变性以及外界干扰等因素的影响，针对各个时间点上数据受影响程度不同的情况，提出一种基于高斯过程预估模型的时间序列数据离群点检测方法。将监测数据分解为标准值和偏差项两个部分，除了对理想情况下的标准值建模，还再次使用高斯过程实现对异方差偏差项的有效描述，通过变分推断解决引入偏差项后的后验概率求解问题，将后验分布中设定的容差区间用于离群点判定。使用雅虎公司公开的网络流量时序数据进行验证，模型输出的容差区间在不同时间点上的变化趋势与标注的正常数据偏差情况相符，并在对比实验中异常检测性能指标F1-score优于自回归积分滑动平均模型、一类支持向量机以及基于密度并伴随噪声的空间聚类算法。实验结果表明，该模型能够有效描述各个时间点上正常数据的分布情况，取得误报率和召回率两方面的综合权衡，而且可以避免模型参数设置不当导致的性能问题。     

混合多个SVR模型的金融时间序列预测

基于支持向量回归(SVR)进行金融时间序列预测,使用PSO算法确定SVR超参数,并用实验的方法选择合适的SVR输入向量。为了解决金融时间序列非平稳性导致的单一SVR模型预测精度不稳定的问题,提出一种混合多个SVR模型的预测算法,选取训练数据的不同子集训练出多个SVR模型,采用对多个模型的预测结果加权求和的方法进行预测,各个模型的权重根据其预测误差动态调整。在全球5大股指上的实验表明,该算法的预测能力明显优于单一SVR模型。     

时间序列分析方法及ARMA,GARCH两种常用模型

证券市场具有数据单一性（大量不需要经过特殊处理的数据）、分析手段多样性和隐蔽性的特点,且与其飞速发展不相称的是证券分析技术进展的缓慢。股市系统中时间序列的预测问题具有重要的理论及实际意义,时间序列的获取是通过对数据库中数据进行分类汇总分析而获得。获取时间序列数据以后可以对它进行预测分析,从而较准确地预见系统的演进。文中介绍了时间序列的基本知识,同时比较了ARMA和GARCH两种常用模型,得出对于中国股市,GARCH模型性能优于ARCH模型。     

时间序列分析方法及ARMA，GARCH两种常用模型

证券市场具有数据单一性（大量不需要经过特殊处理的数据）、分析手段多样性和隐蔽性的特点,且与其飞速发展不相称的是证券分析技术进展的缓慢。股市系统中时间序列的预测问题具有重要的理论及实际意义,时间序列的获取是通过对数据库中数据进行分类汇总分析而获得。获取时间序列数据以后可以对它进行预测分析,从而较准确地预见系统的演进。文中介绍了时间序列的基本知识,同时比较了ARMA和GARCH两种常用模型,得出对于中国股市,GARCH模型性能优于ARCH模型。     

基于均值-方差模型的Relief特征选择优化算法

Relief是公认的效果较好的filter式特征评估方法,但存在特征权值随样本波动的问题,导致识别准确率的下降。提出了一种基于均值-方差模型的特征权值优化算法,采用样本区分能力的平均贡献值的期望和组合贡献值的波动作为特征评估的依据,使得特征选择的结果更加稳定与准确。基于实地采集的地面运动目标的震动信号进行特征选择与分类学习实验,结果表明,该算法得到的特征子集比Relief具有更好的目标区分能力。     

风险资产收益序列相关的多阶段均值-方差投资组合选择

基于多阶段均值-方差框架, 研究任意多种风险资产存在一般收益序列相关时的投资组合选择问题. 首先, 采用Lagrange 对偶原理与动态规划相结合的方法对模型进行求解, 得到多阶段均值-方差模型的有效投资策略和有效边界的解析表达式; 然后, 证明在含有无风险资产的情形下有效边界仍为均值-标准差平面上的一条射线; 最后, 应用所得结论给出一个具体的实例分析.

     

Stability analysis of RBF network-based state-dependent autoregressive model for nonlinear time series

Varying-coefficient models have attracted great attention in nonlinear time series analysis recently. In this paper, we consider a semi-parametric functional-coefficient autoregressive model, called the radial basis function network-based state-dependent autoregressive (RBF-AR) model. The stability conditions and existing conditions of limit cycle of the RBF-AR model are discussed. An efficient structured parameter estimation method and the modified multi-fold cross-validation criterion are applied to identify the RBF-AR model. Application of the RBF-AR model to the famous Canadian lynx data is presented. The forecasting capability of the RBF-AR model is compared to those of other competing time series models, which shows that the RBF-AR model is as good as or better than other models for the postsample forecasts.     

Exploiting the interpretability and forecasting ability of the RBF-AR model for nonlinear time series

In this paper, we explore the radial basis function network-based state-dependent autoregressive (RBF-AR) model by modelling and forecasting an ecological time series: the famous Canadian lynx data. The interpretability of the state-dependent coefficients of the RBF-AR model is studied. It is found that the RBF-AR model can account for the phenomena of phase and density dependencies in the Canadian lynx cycle. The post-sample forecasting performance of one-step and two-step ahead predictors of the RBF-AR model is compared with that of other competitive time-series models including various parametric and non-parametric models. The results show the usefulness of the RBF-AR model in this ecological time-series modelling.     

A time integration algorithm based on the state transition matrix for structures with time varying and nonlinear properties

A variable order method of integrating the structural dynamics equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. When the time variation of the system can be modeled exactly by a polynomial it produces nearly exact solutions for a wide range of time step sizes. Solutions of a model nonlinear dynamic response exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with solutions obtained by established methods.     

Unsupervised learning algorithm for time series using bivariate AR(1) model

Currently, there is an increased interest in time series clustering research, particularly for finding useful similar time series in various applied areas such as speech recognition, environmental research, finance and medical imaging. Clustering and classification of time series has the potential to analyze large volumes of data. Most of the traditional time series clustering and classification algorithms deal only with univariate time series data. In this paper, we develop an unsupervised learning algorithm for bivariate time series. The initial clusters are found using K-means algorithm and the model parameters are estimated using the EM algorithm. The learning algorithm is developed by utilizing component maximum likelihood and Bayesian Information Criteria (BIC). The performance of the developed algorithm is evaluated using real time data collected from a pollution centre. A comparative study of the proposed algorithm is made with the existing data mining algorithm that uses univariate autoregressive process of order 1 (AR(1)) model. It is observed that the proposed algorithm out performs the existing algorithms.     

A time series and reduction‐based model for modeling and QoS prediction of service compositions

Web services are emerging as a major technology for deploying automated interactions between distributed and heterogeneous applications. The accurate prediction of their quality of service (QoS) is important because their users rely on it to decide whether they meet the QoS requirement. The existing studies of QoS prediction usually assume that QoS of service activities follows certain distributions. These distributions are used as static model inputs into stochastic process models to obtain analytical QoS results. Instead, we consider the QoS activities to be fluctuating and introduce a dynamic framework to predict the runtime QoS by employing an Autoregressive Moving Average Model and QoS reduction rules. In the case study of a real‐world composite service sample, a comparison between existing approaches and the proposed one is presented, and results suggest that the proposed one achieves higher prediction accuracy.Copyright © 2014 John Wiley & Sons, Ltd.