两类时间序列模型的异常值检测研究

发布时间：2018-04-12 22:21

本文选题：异常值 + 贝叶斯方法　；参考：《首都经济贸易大学》2016年博士论文

【摘要】：时间序列的异常值检测是时间序列分析中的一个重要研究方向,它能够为不同领域的实际问题提供很多重要信息。整值时间序列和多元时间序列是时间序列分析的重要组成部分,广泛存在于交通、医学、金融等各个领域。因此,研究整值时间序列和多元时间序列的异常值检测对异常值检测理论的发展及解决相关社会实际问题都有着重要的理论和实践意义。然而,广泛深入的文献研究结果显示,当前主流的时间序列异常值检测方法基本上都是针对ARMA或ARIMA模型的,即假定变量为一元连续型的随机变量,对现实生活中广泛存在的不是一元连续型的时间序列数据,特别是对整值时间序列或多元时间序列数据的异常值检测研究严重不足。一阶整值自回归(INAR(1))模型和向量自回归(VAR)模型分别是描述整值时间序列和多元时间序列最为成功的模型。这两个模型的简单性和易解释性使其成为整值时间序列分析和多元时间序列分析的重要工具。鉴于以上因素,本文重点研究了INAR(1)模型和VAR模型这两类时间序列模型的异常值检测。本文的主要研究工作如下:第一,介绍并且对比了现有时间序列异常值检测方法。首先介绍了时间序列模型的概念和特征,以及常见的异常值的概念和类型。其次介绍了似然比检验、影响分析法以及贝叶斯方法三种常见的异常值检测方法,随后对这三种方法进行了模拟实验对比研究。最后说明这几种方法各自的优缺点。第二,研究了同时包含加性异常值(AO类)和新息异常值(IO类)的INAR(1)模型。定义了同时包含AO类和IO类异常值的INAR(1)模型,给出当模型中含有一个AO类和一个IO类异常值,并且这两个异常时刻(不相邻)已知时,参数的条件最小二乘(CLS)估计,证明了它们的唯一性、一致收敛性和渐近正态性,并且说明可以将上述结果推广到模型中含有有限个AO类和有限个IO类异常值的情况。第三,提出了对INAR(1)模型进行异常值检测的贝叶斯方法。此方法可以识别异常值发生的时刻并判别其异常类型为AO类或IO类,同时可以估计参数和异常大小。该方法应用时也不需要提前知道异常值的类型和个数。本文还进行了大量的模拟实验,并应用服务器IP访问数据进行了研究,验证了该方法的有效性。最后,提出了对VAR模型异常值检测的贝叶斯方法。本文将已有贝叶斯方法对AR模型的参数估计和异常值检测推广到VAR模型。基于VAR模型的模拟数据,用贝叶斯方法与似然比检验方法进行了异常值检测的对比研究,结果显示贝叶斯方法优于似然比检验法。最后,将本章所提的贝叶斯异常值检测方法用于对实际宏观经济数据的研究,结果表明该方法是可行的。
[Abstract]:The detection of outliers in time series is an important research direction in time series analysis. It can provide a lot of important information for practical problems in different fields.Integral time series and multivariate time series are important components of time series analysis, which are widely used in transportation, medicine, finance and other fields.Therefore, it is of great theoretical and practical significance to study the outlier detection of integral time series and multivariate time series for the development of outlier detection theory and the solution of relevant social practical problems.However, extensive and in-depth literature research results show that the current mainstream time series outlier detection methods are basically aimed at ARMA or ARIMA models, that is to say, the variables are assumed to be mono-continuous random variables.There is a serious shortage of research on outlier detection of time series data which are not monadic and continuous in real life, especially for integral-valued time series or multivariate time series data.The first order integro-valued autoregressive (INAR1) model and the vector autoregressive (VAR) model are the most successful models for describing the integer time series and multivariate time series, respectively.The simplicity and interpretability of these two models make them an important tool for integer time series analysis and multivariate time series analysis.In view of the above factors, this paper focuses on the detection of outliers in two kinds of time series models: INAR1) model and VAR model.The main work of this paper is as follows: firstly, the methods of outlier detection in time series are introduced and compared.Firstly, the concept and characteristics of time series model and the concept and types of common outliers are introduced.Secondly, three common outliers detection methods, such as likelihood ratio test, influence analysis method and Bayesian method, are introduced.Finally, the advantages and disadvantages of these methods are explained.Secondly, we study the INAR1) model with both additive outliers (AO) and innovation outliers (Io).The INAR1) model containing both AO class and IO class outliers is defined. When the model contains an AO class and an IO class outlier value, the conditional least square (CLS) estimation of the parameters is given when the two outliers are known.Their uniqueness, uniform convergence and asymptotic normality are proved, and it is shown that the above results can be extended to the case where there are finite AO class and finite IO class outliers in the model.Thirdly, a Bayesian method is proposed to detect the outliers of the INAR1) model.This method can recognize the time when the outliers occur and judge whether the abnormal types are AO or IO classes. At the same time, the parameters and the size of the anomalies can be estimated.The method does not need to know the type and number of outliers in advance.In this paper, a large number of simulation experiments are carried out, and the application of server IP access data is studied to verify the effectiveness of this method.Finally, a Bayesian method for detecting outliers of VAR model is proposed.In this paper, the parameter estimation and outlier detection of AR model based on Bayesian method are extended to VAR model.Based on the simulation data of VAR model, the Bayesian method is compared with the likelihood ratio test method to detect outliers. The results show that the Bayesian method is superior to the likelihood ratio test method.Finally, the Bayesian outliers detection method proposed in this chapter is used to study the actual macroeconomic data. The results show that this method is feasible.
【学位授予单位】：首都经济贸易大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：F224

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