演化门限ARMA模型方法与应用

在工程实践中，有许多非线性现象,例如极限环现象、共振跳跃现象、幅频依赖现象等，这些现象实质上是不同非线性系统所表现出的不同特征,门限自回归模型(TARMA)具有很强的通用性，能解释上述非线性现象，并具有一定物理意义的特点,广泛地应用于时间序列建模,针对非线性ARMA模型，提出了演化TARMA算法,该算法克服了传统的H．Tong、D．D．C、局部区间搜索等方法一些缺陷，能自动识别模型所属类型(线性还是非线性)、模型的阶数、模型的相关参数(门限区间参数、门限参数及相应的ARMA模型参数)等。实验结果表明，该方法是高效的、全局的、自适应的、鲁捧的。并且，由于随机性的存在使得所建模型很丰富，便于决策者从中选取合适的模型进行时问序列分析和物理解释，从而显示了其自动化的一面。

Methods and Application of Evolutionary TARMA Modeling

There are many non-linear phenomena in engineering applications, such as limit loop, resonate jumping phenomenon, range frequency depending phenomenon etc., and these phenomena are materially different characteristics of different non-linear systems. Threshold automatic regression model (TARMA) has been widely used in time series modeling because it has the character of generality and can explain the phenomena cited above with physics meaning. Evolutionary TARMA modeling algorithm is proposed which can overcome some limitations of traditional methods including H. Tong method, D.D.C method and local research method. The algorithm can also identify the type of model(linear or non-linear), order number of model and some relevant parameters(threshold interval parameter, threshold parameter, and the corresponding parameters of ARMA model) etc. The experiments show that the algorithm is effective, global, self-adaptive and robust. Moreover, the models constructed are abundant because of the existence of randomness, so decision makers can select appropriate models to analyze time series or explain physically, which has the characteristics of automatization.