基于模糊理论的时间序列预测研究

发布时间：2018-10-26 17:09

【摘要】：由于时间序列预测能够为人们提供良好的决策支持,使其在众多领域得到广泛应用。为了能够对数据不完整和含糊的情况进行预测,模糊时间序列被提出。随着数据时代的到来,时间序列和模糊时间序列模型受到了越来越多的关注。本文在对模糊时间序列和时间序列预测模型的研究基础之上,得到了一些新的结果和研究方法,主要包括如下几个方面的工作：1.随着信息化的深入发展,过分强调精确性而可解释性较差的预测模型已经不能完全满足时间序列预测的实际应用需求。这就迫切需要提出具有高准确率的同时还具有可解释性的时间序列预测模型。针对上述问题,提出基于自动聚类和公理模糊集的模糊时间序列预测模型。该模型利用自动聚类算法根据样本的分布情况产生不同长度的划分区间,克服了静态区间长度的缺点。并利用AFS分类器产生模糊趋势的语义解释,使得预测模型更容易被人理解。在预测的过程中能够得到模糊趋势,这为决策者提供了可靠的依据。然后,将模糊时间序列和经典时间序列分析结合,提出一个基于趋势预测和自回归模型的模糊时间序列预测模型。该模型能够挖掘时间序列中显著的变化趋势,并利用AR(2)模型确定预测数据的波动量,从而得到最终的预测值。将提出的两个模糊时间序列预测模型分别应用到现实中的时间序列上,并将实验结果与其他同类预测模型进行比较,得到了较好的预测结果。2.分别结合模糊数据挖掘和模糊聚类提出两个单步时间序列预测模型。在第一个模型中,根据越新发生与现在的关系越密切的原则,利用仿射传播算法对子序列进行聚类,从而确定最后的子序列所属的类别,即找到与预测样本关系最密切的子序列类。在此基础上,利用模糊数据挖掘技术产生语义规则,并将得到的规则用于预测,这使得预测过程更透明更容易被人们理解。在第二个模型中,结合模糊聚类提出一个新的时间序列预测模型。首先,为了克服传统聚类算法对数据维度的限制,同时能更准确地度量时间序列之间的相似性,提出基于动态弯曲的模糊C-均值聚类算法。然后,利用此算法对构造的时间序列数据进行聚类,并根据聚类结果实施预测。所提出的两个单步时间序列预测模型都被应用到台湾股指时间序列上,实验结果表明了模型的有效性,并得到比同类模型更好的预测结果。3.随着人们研究的深入,多步预测比单步预测有着更重要的理论和实用价值。基于信息粒和模糊聚类提出一个多步(长期)时间序列预测模型。信息粒化将时间序列分割(抽象)成若干有意义可操控的信息粒,这使得时间序列以更容易理解的方式呈现。因此,利用信息粒化构造时间序列预测模型,使得预测模型具有可解释性。由于预测模型是多步预测,一次可以预测出多个预测值,不需要反复迭代,大大减少了计算时间。以人工合成时间序列为例展示了预测模型的应用过程,以此验证了模型的可行性。将该模型应用到多组真实的时间序列上,实验结果显示出了该模型的优越性。
[Abstract]:Because the time series prediction can provide good decision support for people, it has been widely used in many fields. In order to be able to predict incomplete and ambiguous data, a fuzzy time series is proposed. With the advent of data age, time series and fuzzy time series model have been paid more and more attention. Based on the research of fuzzy time series and time series prediction model, some new results and research methods are obtained, including the following aspects: 1. With the in-depth development of information, too much emphasis is placed on the accuracy and the poor prediction model can not completely meet the actual application needs of time series prediction. There is an urgent need to propose a temporal sequence prediction model with high accuracy and an interpretable temporal sequence. In view of the above problems, a fuzzy time series prediction model based on automatic clustering and axiomatic fuzzy sets is proposed. The model utilizes the automatic clustering algorithm to generate different length division intervals according to the distribution of the samples, and overcomes the defect of the length of the static interval. The semantic interpretation of fuzzy tendency is generated by AFS classifier, which makes the prediction model easier to understand. Fuzzy trends can be obtained in the prediction process, which provides a reliable basis for decision makers. Then, combining fuzzy time series and classical time series analysis, a fuzzy time series prediction model based on trend prediction and autoregressive model is proposed. The model can dig a significant change trend in the time series, and use the AR (2) model to determine the fluctuation of the prediction data, so as to obtain the final forecast value. The two fuzzy time series prediction models are respectively applied to the real time series, and the experimental results are compared with other similar prediction models, and a better prediction result is obtained. Two single-step time series prediction models are proposed in combination with fuzzy data mining and fuzzy clustering. In the first model, according to the principle of closer relationship between the new occurrence and the present relationship, the sub-sequence of the last sub-sequence is determined by using the affine propagation algorithm so as to determine the category to which the last sub-sequence belongs, i.e. to find the sub-sequence class closest to the predicted sample relation. On this basis, the fuzzy data mining technology is used to generate semantic rules, and the obtained rules are used for prediction, which makes the prediction process more transparent and easier to understand. In the second model, a new time series prediction model is proposed in combination with fuzzy clustering. Firstly, in order to overcome the limitation of the traditional clustering algorithm on the data dimension, the similarity between the time series can be more accurately measured, and a dynamic bending-based fuzzy C-means clustering algorithm is proposed. Then, the time series data constructed by this algorithm is used to gather the data, and the prediction is carried out according to the result of the poly. Both single-step time series prediction models are applied to the Taiwan stock index time series. The experimental results show the validity of the model and get better prediction results than those of the same model. With the in-depth study, multi-step prediction has more important theoretical and practical value than single-step prediction. A multi-step (long-term) time series prediction model is proposed based on information particle and fuzzy clustering. Information Granularization divides the time sequence (abstracted) into a number of meaningful controllable information particles, which render the time series presented in a more understandable way. Therefore, using the information grain structure time series prediction model, the prediction model has interpretability. Because the prediction model is multi-step prediction, a plurality of prediction values can be predicted at one time, repeated iterations are not needed, and the calculation time is greatly reduced. In this paper, the application process of the prediction model is presented in a synthetic time series as an example, and the feasibility of the model is verified. The model is applied to several sets of real time series, and the experimental results show the superiority of the model.
【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O211.61

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