多元长记忆时间序列近似因子模型分析

发布时间：2018-02-11 02:32

本文关键词： 长记忆性长记忆误差项近似因子模型 VARFIMA模型　出处：《浙江财经大学》2017年硕士论文　论文类型：学位论文

【摘要】：金融时间序列的研究是时间序列研究的一个重要分枝。金融时间序列既有在时间序列大框架下的共性,同时又有区别于其他序列的特性,比如数据的分布往往呈现出尖峰厚尾的特点,数据波动的异方差性以及波动集聚性,自相关性,长记忆特征等等。研究者对于长记忆性的认识起源于自然科学,深耕于经济、金融等领域。本文主要所研究的对象是包含长记忆特征的多维时间序列。本文的目的在于对多维长记忆时间序列进行近似因子模型分析,确定因子个数。对于此,本文在近似因子模型的框架下,针对存在长记忆性的多维时间序列,提出存在长记忆误差项的近似因子模型,并提出了确定该模型中因子个数的估计方法,通过理论和模拟呈现了该方法具有估计一致性的特点。模拟中表明,在不同的长记忆参数下,该估计方法表现出稳健性。在实证中,本文首先研究了全球股票市场之间的联动关系。其次研究了中国股票市场中二十个行业板块指数,运用本文所提出的模型来确定这些行业板块指数因子的个数。本文的主要创新和贡献集中在建立了存在长记忆误差项的近似因子模型,这是对当前近似因子模型的一个拓展,因为已有的近似因子模型,考虑的是误差项的序列相关和截面相关的情况,还未在因子模型中考虑误差项的长期相依性。同时,本文提出了该模型中因子个数的估计方法。这一估计方法主要分为两步,首先,将原时间序列进行长记忆性分解,得到长记忆部分和非长记忆部分。随后用近似因子模型的方法对非长记忆部分进行因子个数的选取,在这一步中,基于BIC和IC准则,提出了估计因子个数新的准则。理论结果证明该估计方法可以一致地估计出真实的因子个数。在统计模拟中,将本文提出的方法同直接使用IC、AIC和BIC准则选取因子的方法做比较。模拟结果发现,当长记忆参数值较大时,本文提出的方法可以准确地估计出真实的因子的个数,并且要远远好于其他方法。当长记忆参数值较小时,本文提出的方法略微逊色使用IC方法,但是仍然可以较为准确地估计出因子个数。总体来说,本文提出的方法对于不同的长记忆性参数,估计值表现出良好的稳健性,平均表现优于通过AIC,BIC和IC准则来确定因子个数。
[Abstract]:The study of financial time series is an important branch of time series research. For example, the distribution of data often shows the characteristics of peak and thick tail, heteroscedasticity and agglomeration of data fluctuations, autocorrelation, long memory characteristics and so on. The purpose of this paper is to analyze the multidimensional long memory time series with approximate factor model and determine the number of factors. In this paper, an approximate factor model with long memory error term is proposed for multidimensional time series with long memory, and a method to estimate the number of factors in the model is proposed. The theory and simulation show that the method is consistent in estimation. The simulation shows that the method is robust under different long memory parameters. This paper first studies the linkage between global stock markets, and then studies 20 industry sector indices in Chinese stock markets. The main innovation and contribution of this paper is to establish an approximate factor model with long memory error term, which is an extension of the current approximate factor model. Because of the existing approximate factor model, the sequence correlation and cross-section correlation of the error term are considered, and the long-term dependence of the error term has not been considered in the factor model. In this paper, a method for estimating the number of factors in the model is proposed. The method is divided into two steps. Firstly, the original time series are decomposed into long memory. The long memory part and the non long memory part are obtained. Then the approximate factor model is used to select the number of factors for the non long memory part. In this step, based on the BIC and IC criteria, A new criterion for estimating the number of factors is proposed. The theoretical results show that the method can estimate the number of real factors consistently. The method proposed in this paper is compared with the method of selecting factors by using ICG AIC and BIC criterion directly. The simulation results show that when the value of long memory parameter is large, the method presented in this paper can accurately estimate the number of real factors. And it is much better than other methods. When the value of long memory parameter is small, the method proposed in this paper is slightly inferior to the IC method, but it can still estimate the number of factors more accurately. The method presented in this paper shows good robustness for different long memory parameters, and the average performance is better than that of determining the number of factors by AICBIC and IC criteria.
【学位授予单位】：浙江财经大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F831.51

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