贝叶斯LASSO在平稳时间序列模型中的应用及实证研究

发布时间：2018-03-21 22:03

本文选题：贝叶斯　切入点：LASSO　出处：《西南财经大学》2014年硕士论文　论文类型：学位论文

【摘要】：随着中国经济和金融环境不断地开放,经济金融方面的海量高维数据的不断积累,大数据时代已经到来。不仅大数据有其本身的价值,而且针对大数据进行建模分析的应用价值也越来越明显。一般来说,面对着同一数据,研究人员可能会有许多可供选择的模型,如何从较多模型中选择出具有应用价值的模型成为了理论界和实证界一直以来所共同关注的焦点。在1980年以前,统计学家对于模型选择的研究方向较多地集中在信息准则方面,比如AIC、BIC和Cp准则,它们的原理简单但计算的维度较高,当变量较多的时候,如果要在所有的可能模型中选择出满足特定准则最小的模型,这类方法面临着实际的操作难度。因此,一个能够大幅度地减少搜寻次数并且具有一定理论优势的研究方法开始被提出,其中Tibshirani(1996)所提出的Least Absolute Shrinkage and Selection Operation(简称LASSO)方法,不仅可以避免最小二乘法在高维条件下的不稳定性,而且还能将不显着的参数自动估计为零,达到模型选择的目的,因此逐渐地成为了众多研究者选择模型的主要方法之一,其中,Efron(2004)提出的最小小角回归(Iars)算法是目前比较流行的解决LASSO的快速而有效的方法之一。由于LASSO方法在一定条件下等价于贝叶斯方法,因此,从贝叶斯的角度考虑模型选择的研究也成为一种新的方向。而且,随着贝叶斯方法在实践中的应用效果被许多研究者关注,由于LASSO方法可以用一种Laplace先验分布的贝叶斯估计进行表示,因此,贝叶斯LASSO方法(Park,2008)逐渐地被正式地提出和被应用。这种方法的主要特点在于,不仅它具有模型选择的作用,而且还能发挥贝叶斯统计的优点,运用MCMC方法进行参数的逼近估计在经济金融研究领域,研究者们普遍面对的数据是时间序列,针对时间序列的建模方法有许多,其中平稳时间序列中三种基本方法即：AR模型、ARMA模型和ARCH模型。目前,从本论文所研读的最新文献来看,时间序列模型中采用LASSO方法的研究已有少许,但尝试性地探讨贝叶斯LASSO方法在平稳时间序列模型中应用效果的研究几乎没有。基于这样的理论和现实背景,本文尝试将贝叶斯LASSO方法应用于平稳时间序列模型中。本文主要从理论和实证两个方面研究了贝叶斯LASSO在平稳时间序列模型中的应用效果。理论方面,首先,本文从平稳时间序列基本方法、LASSO的发展和应用现状、贝叶斯LASSO的发展和应用现状等三个方面综述了已有的研究成果,并讨论了贝叶斯LASSO方法在平稳时间序列模型中的推广的可能性及意义所在,形成本文的理论基础。其次,本文从LASSO的基本思想、贝叶斯基本原理和贝叶斯LASSO方法三个方面,逐层次地将LASSO和贝叶斯紧密地联系在一起。再次,本文分别详细介绍了三种基本平稳时间序列模型：AR模型、ARMA模型和ARCH模型,并通过数据变换的处理方式,成功地从理论上说明贝叶斯LASSO方法应用到上述三种模型中的可行性。最后,通过R软件平台,本文应用现有的贝叶斯LASSO算法,分别将贝叶斯LASSO方法应用在AR模型、ARMA模型和ARCH模型的数据模拟分析之中,验证了三种模型的模拟应用的效果。实证方面,本文主要输入了上证300指数的数据,对指数的日对数收益率数据进行了波动率的ARCM建模分析,并将实证结果与一般的ARCM模型进行了对比,结果表明本文的方法在ARCM波动率实证研究中的尝试具有一定的可行性效果。本文的主要结论包括： (一)平稳时间序列模型的估计可以运用贝叶斯LASSO方法进行解决,并能够取得一定的效果,但并非总是优于LASSO。因为,本论文的数据模拟分析发现,在适当的样本容量条件下,本文方法的正确率在有的条件下对某些参数而言是高于LASSO方法的,有的条件下也是低于LASSO的。 (二)贝叶斯LASSO方法能够提供更多的概率决策信息。因为,本文所采用的方法属于贝叶斯框架的分析方法,故可以提供更可靠的区间估计等信息。本论文的算法是通过MCMC模拟确定了样本后验分布的稳定性,我们从该分布中分析出很多的信息,如本文所定义的“变量接受概率”,它可以根据实际情况根据样本量和时间序列维数进行合理的设置,当样本量比较大的时候,设置较高的接受概率可以准确选择出合理的变量,当样本量逐渐下降的时候,某些参数的变量接受概率会随着样本量的下降而不断降低。
[Abstract]:With the China economic and financial environment constantly open, the accumulation of massive high-dimensional data of economic and financial aspects of the era of big data has arrived. Not only big data has its own value, but also the application value of the modeling and analysis for big data is becoming more and more obvious. In general, faced with the same data, researchers may there will be many alternative models, how to choose from the many models of the model value has become the focus of theoretical and empirical circles has been a common concern. Before 1980, statisticians for more research direction of model selection on information standards, such as AIC, BIC and Cp criterion. The principle is simple but the computation of high dimension, when there are more variables, if possible in all models selected to meet specific criteria of minimum model, facing this kind of method The difficulty of the operation. Therefore, one can greatly reduce the search times and the research method has certain theoretical advantages was proposed, in which Tibshirani (1996) proposed by Least Absolute Shrinkage and Selection Operation (LASSO) method can not only avoid the least squares method in high dimension under the condition of instability zero automatic parameter estimation but also will not be significant, achieve the purpose of model selection, thus gradually become one of the main methods, many researchers choose to model the Efron (2004) proposed the minimum small angle regression (Iars) algorithm is a popular solution for LASSO rapid and effective method of.
Because the LASSO method under certain conditions is equivalent to the Bayesian method, therefore, from the point of view of Bayesian model selection has become a new direction. Moreover, with the application of Bayesian method in practice by many researchers, because LASSO method can estimate that with a prior distribution in Bayesian Laplace therefore, Bayesian LASSO method (Park, 2008) has been formally put forward and is applied. The main characteristic of this method is that it not only has the model choice for the role, but also play the advantages of Bayesian statistics, using MCMC method of parameter estimation approach in the economic field of financial research, researchers generally face data is the time series, according to the modeling method of time series are many, including three kinds of basic methods of stationary time series: AR model, ARMA model and ARCH model. First, from the latest literature in this thesis study, LASSO method is used in time series model has a little research, but the study attempts to explore Bias LASSO method application in stationary time series model hardly. Based on this theoretical and practical background, this paper tries to Bias LASSO method is applied to stationary time the sequence of the model.
This paper mainly from two aspects of theory and empirical research on the application of Bias LASSO in the stationary time series model. The theory, first, from the basic method of stationary time series, the development and application status of LASSO, the three aspects of Bias LASSO's development and application of the existing research results, are discussed. Bias LASSO method in stationary time series model in the promotion of the possibility and significance of the formation of the theoretical basis of this paper. Secondly, this article from the basic idea of LASSO, the three aspects of the basic principle of Bias and Bias LASSO method, by level LASSO and Bias closely together. Thirdly, this paper introduces in detail three basic stationary time series models: AR model, ARMA model and ARCH model, and through the processing method of data transformation, successfully explains Bias LASSO theoretically. The method applied to the feasibility of the three models. Finally, through the R software platform, this paper uses Bias existing LASSO algorithm, respectively, the application of Bias method in the LASSO AR model, ARMA model and ARCH model of data simulation, to verify the three models to simulate the application effect. The empirical aspect, this paper enter the Shanghai 300 index data was analyzed by ARCM modeling the volatility of daily logarithmic return rate index data, and empirical results and the general ARCM model were compared. The results show that this method has certain effect to rate the feasibility in empirical research on the ARCM wave.
The main conclusions of this paper include:
(a) estimation of stationary time series model can be used to solve the Bayesian LASSO method, which can obtain a certain effect, but is not always better than that of LASSO. because the data analysis found that in the condition of sample size is proper, the correct rate of this method is higher than that of LASSO method for some parameters in some conditions under some conditions is less than LASSO.
(two) Bias LASSO method can provide more information for probabilistic decision analysis method, this method belongs to the Bias framework, it can provide more reliable information of interval estimation. The algorithm is proved the stability of distribution determines the sample through MCMC simulation, we analyze a lot of information from the the distribution, as defined herein "variable acceptance probability", it can according to the actual situation according to the sample size and the dimension of time series reasonable setting, when the sample size is relatively large, a higher probability of acceptance can accurately select the reasonable variables, when the sample size decreases gradually, some parameters variable acceptance probability will continue to decrease with the decrease of sample size.

【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：O211.61;F830.91

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