基于小波多尺度分析的GARCH建模方法的拓展  

Expansion of modeling method for GARCH based on wavelet multi-scale analysis

作　　者：彭选华[1] 傅强[1] 

机构地区：[1]重庆大学经济与工商管理学院,重庆400044

出　　处：《系统工程理论与实践》2011年第11期2060-2069,共10页Systems Engineering-Theory & Practice

基　　金：高等学校博士学科点专项科研基金(20100191110033);国家自然科学基金(70501015)

摘　　要：考虑到交易周期对资产价格波动特征的重要影响,将小波多尺度分析引入广义自回归条件异方差(GARCH)建模理论,提出了多尺度广义自回归条件异方差模型和多尺度增广分整广义自回归条件异方差均值模型,同时通过改进迭代的步长参数,得到了收敛速度快于BHHH算法的数值优化方法.对上证综合指数进行实证分析,结果表明:该模型克服了GARCH理论无法同时揭示蕴含在资产价格内部的多时间尺度信息的缺陷,还能够捕获到资产收益率在不同时间尺度上的局部波动特征;改进后的算法对模型参数估值效果十分明显.这类模型有助于探究资产价格伴随交易周期演化的微观动力学机制.Considering the important influence of the transaction cycle on the volatility characteristics of asset price, this paper introduced the wavelet multi-scale analysis into the GARCH theory, and proposed a multi-scale GARCH and multi-scale Augmented-FIGARCH-M model respectively. Meanwhile,we improved the iteration step length to obtain a numerical optimization algorithm which had better convergence and stability compared with the BHHH algorithm. Conclusions supported by the empirical analysis of Shanghai composite index are： The models overcome the shortcomings of traditional GARCH theory in discovering the information of multi-time scales contained in the price, and capture the volatility characteristics of the return in different time scales; It is obviously effective to use the improved algorithm to estimate the models parameter. The above models may help to explore the micro dynamic mechanism of asset price with the transaction cycle evolution.

关 键 词：GARCH 增广FIGARCH—M 多尺度分析 最大重复离散小波变换 

分 类 号：F224.0[经济管理—国民经济]