改进型前向神经网络的时间序列预测及其性能比较

【作者】 戴群；

【导师】 陈松灿；

【作者基本信息】 南京航空航天大学 ， 计算机软件与理论， 2003， 硕士

【摘要】 时间序列预测是动态数据分析处理的一个重要方面，在科学、经济、工程等许多应用中都存在着在历史数据的基础上预测未来的问题。面对自然和社会经济现象中大量存在的非线性、非平稳的复杂时间序列，传统的统计分析方法效果欠佳。自从1987年Lapedes和Farber首先应用神经网络进行预测以来，神经网络预测时间序列方法受到广泛重视。目前，已有多种不同形式的网络被用于工业、经济等的预测中。研究结果表明，神经网络用于预测效果好，为一类高度非线性动态关系的时间序列预测提供了一条有效途径。 在本文中将我们改进的圆形反向传播网络模型(Improved Circular Back Propagation--ICBP)应用于时间序列预测，进行了单步和多步时间序列预测研究。ICBP是我们对圆形反向传播网络(Circular Back Propagation—CBP)的推广，CBP不仅具有良好的推广和自适应能力，而且在其框架下分别构建出矢量量化(VQ)和RBF网络，展示出了极大的灵活性。我们在保持CBP原有结构下，通过对CBP的输入层扩充节点(1个)的特殊构造，以及对该节点与隐层间权值的特殊赋值，获得了较CBP更一般的改进网络模型(ICBP)。经实验证实，ICBP在预测和逼近能力上优于CBP。 但在预测时CBP和ICBP都忽视了时间序列本身的结构性变化及相关性，即没有考虑观察点与预测点的远近对预测性能的影响。打折最小平方(Discounted Least Squares-DLS)原理恰好能刻画这种影响。本文借用该原理实现了DLS-ICBP在时间序列预测上的显著改进。此外，为实现与RBF的比较，构建了基于误差平方准则的DLS-RBF网络作为本文的副产品。 另一方面，传统的p步前向预测的链结构神经网络的预测质量随着p的增加下降很快，这种现象的原因是网络的输入没有为预测提供足够多的信息，而训练步数增多则使信息缺失更多。为此，Duhoux提出了一种新型的链结构神经网络，并通过实验证实新型的链结构改进了多步预测的性能。本文借助这种链结构构成链状的DLS-ICBP网络进行了推广的多步时间序列预测的研究。实验证实基于DLS的新型链结构网络较传统的DLS-ICBP和ICBP链结构网络的多步预测性能有较大提高。 最后，大多数监督学习神经网络是通过最小化训练集的均方差来训练网络，而野值的存在导致这种训练的神经网络模型在预测时会产生极大的不精确性。我们借用LOG鲁棒函数构建了LOG-ICBP网络，进行了存在野值情况时的时间序列预测研究。在LOG-ICBP中平均对数平方误差(MLSE，mean log squared error)取代了均方差(MSE，mean squared error)作为误差准则。实验结果表明LOG-ICBP网络在存在野值情况下的预测效果明显优于ICBP。更多还原

【Abstract】 Time series prediction is an important aspect of dynamic data analysis and processing. There exists the demand of predicting the future based upon historical data in the applications of science,economics and engineering. In the face of the nonlinear and non-stationary time series largely existed in natural and social economical phenomena,the traditional method of statistical analysis performed badly. Since 1987,Lapedes and Farber firstly applied neural networks to time series prediction. Then such a predicting method with neural networks has widely been recognized. Presently,many different types of networks have been proposed and applied to the forecasting in industry and economics. The research results show that neural networks have good performance in prediction,which providing an effective approach for highly nonlinear and dynamic time series forecasting.In this article,we applied our improved circular back-propagation (ICBP) network to single step and multi-steps time series prediction respectively. ICBP is a generalization to circular back-propagation (CBP) network. CBP possesses good generalization ability and adaptability compared with the counterpart BP. And in its frame we can construct vector quantification (VQ) and radial basis function (RBF) networks,showing great flexibility. Keeping the original structure of CBP unchanged,we add an extra node to CBP input level and assign specific values to the weights between that node and the hidden level,and then we obtain a more general model than CBP,which is ICBP. The analysis and simulations all demonstrate the reasonability and superiority of the proposed model.But during predicting,both CBP and ICBP neglected structural changes and correlation in time series themselves. They did not consider how the distance from the observation point to the current predicting point would influence the resulting performance. Discounted least squares principle describes this influence precisely. In this paper the principle is borrowed to construct DLS-ICBP which realizing great improvements in prediction. In addition,in order to compare with RBF,we construct DLS-RBF network as a by-product of this paper.On the other hand,when we use the traditional chained neural networks to predict information p step ahead,the predicting quality declines rapidly with the increment of p. The reason for this phenomenon is that the network inputs did not supply enough information for the future predicting. While the increment of training steps make the information absence become heavier. Duhoux brought forward a new kind of neural network chain and proved through experiments that the new chain improved the effect ofmulti-steps prediction. In this paper we adopt this new chain to construct chained DLS-ICBP network and greatly boost the performance of multi-steps time series prediction.Finally,most supervised learning neural networks train themselves through minimizing mean squared error. But when the neural network models trained in this way are used to do forecasting,the existence of outliers result in great imprecision. We adopt robust method to construct LOG-ICBP network and research time series prediction with outliers. In LOG-ICBP,mean squared error(MSE) is substituted by mean log squared error(MLSE) to be the error criterion. The experiment results show that LOG-ICBP has better predicting effect than ICBP when outliers exist.更多还原