滑动窗口二次自回归模型预测非线性时间序列

提出一种新颖的非线性时间序列预测模型 ,即滑动窗口二次自回归 (MWDAR)模型 .MWDAR模型使用部分的历史数据及其二次项构造自回归模型 .模型参数用线性最小二乘法估计 .应用模型进行预测时 ,预先选定窗口大小以及模型一次项和二次项的阶次 .在每个当前时刻 ,先根据窗口内的数据估计模型参数 ,然后根据输入向量及模型参数做出预测 .这种预测方法不仅适合小数据集的时间序列预测 ,而且对大数据集具有极高的计算效率 .该文分别用H啨ｎｏｎ混沌时间序列数据和真实的股票交易数据作了ＭＷＤＡＲ方法与局域线性化方法的 1步和多步预测对比 ,结果显示MWDAR方法无论在预测精度上 ,还是在计算效率上都优于局域线性化方法 .     

基于灰色关联度准则的TVARMA模型参数估计方法*

针对时变自回归滑动平均模型参数估计问题,基于时间基扩展思想,推导了两种不同的时变自回归滑动平均模型参数估计方法——非线性最小二乘方法和辅助序列法,并以灰色关联度作为观测序列和模型输出序列的相似性评价准则,给出相应的参数迭代估计过程。分别将这两种不同的迭代估计方法应用于某飞行器的结构响应非平稳时间序列的建模,应用结果表明,辅助序列法与非线性最小二乘方法相比,在参数估计精度、收敛特性等方面,前者均优于后者;辅助序列法更适于非平稳时间序列的建模。     

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。     

基于快速小波变换的石英加速度计零偏预测

针对石英挠性加速度计零偏在贮存期间受外界环境影响发生漂移的补偿问题,研究了基于快速小波变换的加速度计零偏预测方法.通过Mallat算法从非平稳的零偏序列中提取出平稳的细节序列和非线性趋势序列,再根据序列的特点分别采用自回归移动平均(ARMA)模型和径向基函数(RBF)神经网络进行预测建模;最后利用小波重构公式得到零偏预测值.为验证所提方法的有效性,对某型加速度计2年贮存条件下的零偏标定值进行了建模仿真.结果显示:组合模型较单一自回归综合移动平均(ARIMA)模型和RBF模型预测精度分别提升45.5％和47.4％.     

一种新的统计预测模型——多项式系数自回归模型

传统的自回归滑动平均模型（ARMA）和新近出现的函数系数自回归模型（FAR）不能满足非线性时间序列预测分析的准确度与运算速度要求,为了改进预测性能,研究提出了一种新的统计预测模型——多项式系数自回归模型（PCAR）。给出了PCAR模型的表示形式,详细探讨了PCAR模型的参数估计和阶次选择方法,在此基础上又提出了基于BIC准则的建模算法。同ARMA模型相比,PCAR模型扩大了适用对象范围,有效降低了模型选择误差;同FAR模型相比,它具有参数模型的特点,避免了系数函数局部线性回归估计所存在的不足;分析了PCAR模型与ARMA、FAR模型的等价条件。通过实验分析得出了PCAR模型较ARMA、FAR模型的单步预测准确度分别提高了99.65%和18.7%的结论,而且PCAR建模运算所需时间仅为FAR模型的0.2%。     

基于ARIMA和LSTM混合模型的时间序列预测

由于现实中的时间序列通常同时具有线性和非线性特征,传统ARIMA模型在时间序列建模中常表现出一定局限性。对此,提出基于ARIMA和LSTM混合模型进行时间序列预测。应用线性ARIMA模型进行时间序列预测,用支持向量回归(SVR)模型对误差序列进行预测,采用深度LSTM模型对ARIMA模型和SVR模型的预测结果组合,并将贝叶斯优化算法用于选择深度LSTM模型的超参数。实验结果表明,与其他混合模型相比,该模型在五种不同时间序列预测中能够有效提高预测精度。     

混合模型在经济时间序列预测中的应用研究

研究经济预测问题,为社会经济发展提供预测依据.由于经济时间序列是一种多维、非线性数据,采用单-的线性或非线性模型都不全面反映特点,导致预测精度不理想.为了提高经济时间序列预测精度,提出一种多变量自回归(CAR)和支持向量机(SVM)相结合的混合预测方法.混合方法首先利用CAR模型对经济时间序列的线性部分进行预测,然后采用支持向量机对非线性部分进行预测,将预测结果组合在-起,得到混合模型的预测结果.实验结果表明,混合模型的预测精度明显优于单独模型;发挥了2种模型的优势,得到一种精度高的经济预测效果.     

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．     

基于小波分析的时间序列数据挖掘

将小波分析和ARMA模型引入时间序列数据挖掘中。利用小波消噪对原始时间序列进行滤波,利用小波变换充分提取和分离金融时间序列的各种隐周期和非线性,把小波分解序列的特性和分解数据随尺度倍增而倍减的规律充分用于BP神经网络和自回归移动平均模型的建模。利用小波重构技术将各尺度域的预报结果组合成为时间序列的最终预报。经过试验验证了该方法的实际有效性。     

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.     

Boosting nonlinear additive autoregressive time series

Several methods for the analysis of nonlinear time series models have been proposed. As in linear autoregressive models the main problems are model identification, estimation and prediction. A boosting method is proposed that performs model identification and estimation simultaneously within the framework of nonlinear autoregressive time series. The method allows one to select influential terms from a large number of potential lags and exogenous variables. The influence of the selected terms is modeled by an expansion in basis function allowing for a flexible additive form of the predictor. The approach is very competitive in particular in high dimensional settings where alternative fitting methods fail. This is demonstrated by means of simulations and two applications to real world data.     

Non-linear time series clustering based on non-parametric forecast densities

The problem of clustering time series is studied for a general class of non-parametric autoregressive models. The dissimilarity between two time series is based on comparing their full forecast densities at a given horizon. In particular, two functional distances are considered: L¹ and L². As the forecast densities are unknown, they are approximated using a bootstrap procedure that mimics the underlying generating processes without assuming any parametric model for the true autoregressive structure of the series. The estimated forecast densities are then used to construct the dissimilarity matrix and hence to perform clustering. Asymptotic properties of the proposed method are provided and an extensive simulation study is carried out. The results show the good behavior of the procedure for a wide variety of nonlinear autoregressive models and its robustness to non-Gaussian innovations. Finally, the proposed methodology is applied to a real dataset involving economic time series.     

A two-step combined algorithm based on NARX neural network and the subsequent prediction of the residues improves prediction accuracy of the greenhouse gases concentrations

Neural Computing and Applications - This paper compares the most applicable models for the forecasting of time series. Models based on artificial neural networks nonlinear autoregressive neural...     

Forecasting ENSO with a smooth transition autoregressive model

This study examines the benefits of nonlinear time series modelling to improve forecast accuracy of the El Niño Southern Oscillation (ENSO) phenomenon. The paper adopts a smooth transition autoregressive (STAR) modelling framework to assess the potentially smooth regime-dependent dynamics of the sea surface temperature anomaly. The results reveal STAR-type nonlinearities in ENSO dynamics, which results in the superior out-of-sample forecast performance of STAR over the linear autoregressive models. The advantage of nonlinear models is especially apparent in short- and intermediate-term forecasts. These results are of interest to researchers and policy makers in the fields of climate dynamics, agricultural production, and environmental management.     

Forecasting time series using a methodology based on autoregressive integrated moving average and genetic programming

The autoregressive integrated moving average (ARIMA), which is a conventional statistical method, is employed in many fields to construct models for forecasting time series. Although ARIMA can be adopted to obtain a highly accurate linear forecasting model, it cannot accurately forecast nonlinear time series. Artificial neural network (ANN) can be utilized to construct more accurate forecasting model than ARIMA for nonlinear time series, but explaining the meaning of the hidden layers of ANN is difficult and, moreover, it does not yield a mathematical equation. This study proposes a hybrid forecasting model for nonlinear time series by combining ARIMA with genetic programming (GP) to improve upon both the ANN and the ARIMA forecasting models. Finally, some real data sets are adopted to demonstrate the effectiveness of the proposed forecasting model.     

A hybrid optimized error correction system for time series forecasting

Time series forecasting is a challenging task in machine learning. Real world time series are often composed by linear and nonlinear structures which need to be mapped by some forecasting method. Linear methods such as autoregressive integrated moving average (ARIMA) and nonlinear methods such as artificial neural networks (ANNs) could be employed to handle such problems, however model misspecification hinders the forecasting process producing inaccurate models. Hybrid models based on error forecasting and combination can reduce the misspecification of single models and improve the accuracy of the system. This work proposes a hybrid system that is composed of three parts: a) linear modeling of the time series, b) nonlinear modeling of the error series, and c) combination of the forecasts using three distinct approaches. The system performs a search for the best parameters of the linear and nonlinear components, and of the combination approaches. Particle swarm optimization is used to find suitable architecture and weights. Experiments show that the proposed technique achieved promising results in time series forecasting.     

Chaotic analysis of predictability versus knowledge discovery techniques: case study of the Polish stock market

Increasing evidence over the past decade indicates that financial markets exhibit nonlinear dynamics in the form of chaotic behavior. Traditionally, the prediction of stock markets has relied on statistical methods including multivariate statistical methods, autoregressive integrated moving average models and autoregressive conditional heteroskedasticity models. In recent years, neural networks and other knowledge techniques have been applied extensively to the task of predicting financial variables.
This paper examines the relationship between chaotic models and learning techniques. In particular, chaotic analysis indicates the upper limits of predictability for a time series. The learning techniques involve neural networks and case–based reasoning. The chaotic models take the form of R/S analysis to measure persistence in a time series, the correlation dimension to encapsulate system complexity, and Lyapunov exponents to indicate predictive horizons. The concepts are illustrated in the context of a major emerging market, namely the Polish stock market.     

A self-organising mixture autoregressive network for FX time series modelling and prediction

Nowadays a great deal of effort has been made in order to gain advantages in foreign exchange (FX) rates predictions. However, most existing techniques seldom excel the simple random walk model in practical applications. This paper describes a self-organising network formed on the basis of a mixture of adaptive autoregressive models. The proposed network, termed self-organising mixture autoregressive (SOMAR) model, can be used to describe and model nonstationary, nonlinear time series by means of a number of underlying local regressive models. An autocorrelation coefficient-based measure is proposed as the similarity measure for assigning input samples to the underlying local models. Experiments on both benchmark time series and several FX rates have been conducted. The results show that the proposed method consistently outperforms other local time series modelling techniques on a range of performance measures including the mean-square-error, correct trend predication percentage, accumulated profit and model variance.