【作者】 李慧君；

【导师】 郑文瑞；

【作者基本信息】 吉林大学 ， 应用统计（专业学位）， 2020， 硕士

【摘要】 现实生活中存在着大量的时间序列数据,它们大多数是围绕时间轴进行排列的数据,这些数据通常都具有一定的规律,通过探索历史数据的内在规律,从而可以得达到预测时间序列数据的目的,最终将其应用到现实生活和生产活动中去,通常这些时间序列数据都具有一定的完整性和精确性,我们称之为经典时间序列数据,经典的时间序列预测模型成立的必要条件是历史的趋势适应于未来的发展。然而,大量的含糊、不精确、不完整的数据还广泛存在于现实世界中,针对这类不完整的数据,模糊时间序列预测模型应运而生,模糊时间序列模型能够解决传统时间序列预测模型无法处理的模糊问题,它的优势就在于处理不确定性和模糊性数据方面,而且模糊时间序列模型拥有比较高的预测精确度。Zadeh在1965年提出模糊集理论后,模糊理论在积累过程中取得了巨大的成就,并被广泛应用到了入学人数、股票价格指数和期货价格、温度和旅游人数等的预测中去。首先,本文在Song等提出的模糊时间序列的概念和预测模型的基础上进行改进。Song等提出的模糊时间序列预测模型通常包括以下几个步骤,分别是:确定和划分论域、对模糊集进行定义和模糊化、模糊关系的选取和模糊规则的建立、数据的去模糊化预测等步。但是经典的模糊时间序列预测模型在论域划分上通常是基于经验或者数据分布进行平均划分论域的,这种方法并不合理,使数据失真且没有最大限度的利用原始数据提供的信息。本文将利用FCM算法(Fuzzy c-means clustering algorithm)对论域进行优化划分,更大限度的利用了历史数据所提供的信息,从而提高了预测精度。利用模糊关系出现的次数建立模糊矩阵,又利用次数对相应的聚类中心进行加权平均得到相应的下一时刻的预测值,最后利用RMSE和MAPE作为评判标准,对模型有效性进行了评估。其次,将模型应用到Alabama大学注册人数预测案例中,并将预测结果与经典的模糊时间序列预测模型的结果进行对比和评价,预测精度明显提高且优于其他模型。然后选取2019年8-10月的黄金期货收盘价格历史数据,利用该模型预测这一时期的黄金期货收盘价格,由结果可知该改进的模型也适用于黄金期货价格预测,对黄金期货投资者和学术界研究市场规律提供了更加有价值的理论,从而将模型推广到更加广泛的应用中去。最后,总结了该预测模型的改进工作,并揭示该模型存在的问题和不足,对接下来需要开展的工作进行展望。做进一步的改进将它与更加复杂的机器学习算法相结合从而达到更精确的预测效果,在提高预测精度的同时也必须考虑到模型的泛化能力,对其进行多步预测或高阶预测也许会是不错的选择。更多还原

【Abstract】 There are a lot of time series data in real life,most of them are arranged around the time axis.These data usually have certain laws.By exploring the internal laws of historical data,we can achieve the purpose of predicting time series data,and finally apply them to real life and production activities.Usually these time series data have There is a certain degree of integrity and accuracy,we call it the classical time series data.The necessary condition for the establishment of the classical time series prediction model is that the historical trend adapts to the future development.However,a large number of vague,imprecise and incomplete data still exist widely in the real world.Aiming at this kind of incomplete data,the fuzzy time series prediction model emerges as the times require.The fuzzy time series model can solve the fuzzy problem that the traditional time series prediction model cannot deal with.Its advantage lies in dealing with the uncertainty and fuzzy data,and the fuzzy time The inter sequence model has high prediction accuracy.After Zadeh put forward the fuzzy set theory in 1965,the fuzzy theory has made great achievements in the accumulation process,and has been widely used in the prediction of enrollment,stock price index,futures price,temperature and tourism number.Firstly,this paper improves the concept and prediction model of fuzzy time series proposed by song et al.The fuzzy time series prediction model proposed by song et al.Usually includes the following steps: determining and dividing the domain,defining and fuzzifying the fuzzy set,selecting the fuzzy relation,establishing the fuzzy rules,and de fuzzifying the data.However,the classical fuzzy time series prediction model usually divides the domain based on experience or data distribution,which is not reasonable,which makes the data distorted and does not make the most of the information provided by the original data.In this paper,the FCM algorithm(fuzzy c-means clustering algorithm)is used to optimize the division of the domain,making greater use of the information provided by historical data,so as to improve the prediction accuracy.The fuzzy matrix is established by the number of fuzzy relations,and the corresponding cluster center is weighted by the number of times to get the corresponding prediction value at the next moment.Finally,RMSE and MAPE are used as the evaluation criteria to evaluate the effectiveness of the model.Secondly,the model is applied to Alabama University Enrollment prediction case,and the prediction results are compared and evaluated with the results of the classic fuzzy time series prediction model.The prediction accuracy is significantly improved and better than other models.Then select the historical data of gold futures closing price from August to October 2019,and use the model to predict the closing price of gold futures in this period.From the results,it can be seen that the improved model is also applicable to the prediction of gold futures price,which provides a more valuable theory for gold futures investors and academic circles to study market rules,so as to promote the model to a wider application.Finally,the paper summarizes the improvement of the prediction model,reveals the problems and shortcomings of the model,and looks forward to the future work.Further improvement is made to combine it with more complex machine learning algorithm to achieve more accurate prediction results.While improving the prediction accuracy,the generalization ability of the model must also be considered.Multi-step prediction or highorder prediction may be a good choice.更多还原