文档介绍：华中科技大学
硕士学位论文
长记忆时间序列的研究与应用
姓名:陈璞
申请学位级别:硕士
专业:数量经济学
指导教师:王少平
20060427
摘要
长期记忆性也称为长期相关性、长期依存性或持久性,它描述的是序列的高阶相
关结构。长期记忆过程的相距甚远的观察值之间仍存在着某种稳定的依存关系,自相
关函数衰减缓慢。作为挑战线性范式金融理论和金融研究的深入,金融时间序列的肥
尾分布、分形结构、混沌行为和长期记忆等非线性特征,是当今最活跃的研究领域之
一。防范与规避金融风险一直以来都是投资理论与实践的主要问题。针对大量经济
时间序列所呈现出长记忆特征,本文重点研究了既能描述收益短记忆性又能刻画长
记忆性风险度量的ARFIMA模型,介绍了有关长记忆时间序列的定义、检验方法、
建模方法等等。本文采用ADF检验和KPSS检验联合的方法以及传统的R/S分析法和
修正的R/S分析法检验我忆特征。各种方法一致支持,深
证和上证收益序列都具有长记忆性,且深圳成指收益过程的记忆长度比上证A指的
强。基于长记忆的检验结果,本文对我国深圳成指和上证A指日收益序列采用
ARFIMA模型检验收益的长记忆,参数估计结果表明收益序列具有长记忆。比较信
息准则发现ARFIMA(2,d,2)是拟合深圳日收益序列长记忆性的最优模型,
ARFIMA(3,d,2)是拟合上证A指日收益序列长记忆性的最优模型。最后得出结论:
我忆性,多种因素在一定程度上导致了我
忆性,缺乏有效性。
关键词:长记忆 R/S分析法 KPSS检验 ARFIMA模型
Abstract
Measuring the risk of a portfolio of financial assets or securities plays an important
role in the field of financial economics. In this paper, the ARFIMA model is introduced to
measure risk. It can describe not only volatility clustering and heteroskedasticity but also
long memory of return process and volatility process, and we introduced the definition、
test method and setting model of long memory time series. Using ADF KPSS test,
classical R/S analysis and modified R/S analysis, we detect long memory of return series
of Shanghai and Shenzhen. The results show that both return series of Shanghai and
Shenzhen have strong long memory. And the long memory of Shenzhen is stronger than
Shanghai. Based on these results, we use ARFIMA model to test the long memory of
Shanghai and Shenzhen return series. And estimations of parameters indicate that there is
long memory in the return series. parisons of Information Criterium demonstrate
that ARFIMA(2,d,2) is most appropriate for Shenzhen and ARFIMA(3,d,2) is most
appropriate for Shanghai. We get the conclusion that there is long memory exist in the
stock market of China. There are many factors make the stock market has long memory
and no efficient.
Key words: long memory R/S analysis KPSS te