基于3σ准则的分段拟合及其GARCH修正模型  

Piecewise Fitting based on 3σGuidelines and its Garch Remaining Modified model

作　　者：林静[1] 唐国强[1] 覃良文 LIN Jing TANG Guo-qiang QIN Liang-wen(College of science, Guilin University of technology, Guilin 541006 ,China)

机构地区：[1]桂林理工大学理学院,广西桂林541006

出　　处：《经济数学》2016年第3期26-32,共7页Journal of Quantitative Economics

基　　金：国家自然科学基金项目(41101136);国家社会科学基金项目(13CJY075);广西财经学院数量经济学重点实验室项目(2014)

摘　　要：在金融时间序列中,一组金融序列可被视为由不同时间段的分段函数拟合连接而成.利用3σ准则确定分段函数的临界点,并根据AIC准则及调整后R2对分段点进行验证,从而分段点把数据分割成两部分.对两序列分别用合适的函数进行拟合,并用ARMA-GARCH模型对残差序列进行修正.由上证综合指数数据的实证分析结果表明:3σ准则能很好地检索出临界点,同时建立的分段函数模型预测效果要优于ARMA与EGARCH模型,以及ARMA-GARCH模型的引入对模型的精确度有所提高.所介绍的方法简单易懂、便于操作、精度高,为金融投资者和学者提供参考价值.In the financial time series, a group of financial sequence can be used as a function, in which piecewise fitting connection is made in different time periods. The Pauta criterion was exploited to determine the critical point of piecewise func- tions, according to AIC guidelines and coefficient of determination after adjustment to test breaking point, thus the staging point split the data into two parts. Two sequences were fitted with the appropriate function, and ARMA-GARCH model was used to amend the residual sequence. The empirical results of Shanghai composite index show that the 3 σ guidelines can retrieve critical point commendably. At the same time, the forecasting efficiency of piecewise function model is better than ARMA mod- el and EGARCH model. Also, the precision of the model is improved by the introduction of ARMA-GARCH model. Moreo- ver, the method is simpIe, easy to understand and operate, and accurate, which provides reference value for financial investors and scholars.

关 键 词：应用统计数学 分段拟合 拉依达准则 GARCH模型 临界点 

分 类 号：F224[经济管理—国民经济]