Vol.6 No.3
Jun.2011
doi
:
10.3969/j.issn.
16734785.2011.03.014
小波变换和GM-ARMA组合模型的股指预测�
吴朝阳�
(康考迪亚大学统计与数学系，蒙特利尔H3G2H9)
摘要：当前在利用小波分解和其他模型建立组合模型的过程中,对小波基方程的选择和分解层数并没有一个标�
准,基本上是通过经验和一些实验来决定这2个因素；而且很多利用小波分解建立的组合模型并不考虑模型之间相�
互的影响,对各个子模型的参数估计采取各自独立的估计,从而导致预测结果不是最优.为此,提出了先对小波基方�
程和分解层数这2个特征进行参数化，然后定量地对所有子模型的特征参数进行统一、综合的评估,以达到建立最�
佳组合模型的目的.由于该组合模型是由小波分解、灰色模型和ARMA模型组合而成的，因此称为WGM-ARMA模�
型.股指预测的实例WGM-ARMA模型大幅度地降低了预测误差,说明了该组合模型的有效性、实用性和可�
行性.�
关键词：小波分解；灰色模型；ARMA模型；GM-ARMA模型；股指预测�
中图分类号:TP18文献标识码:A文章编号:1673-4785(2011 )03-0279-04
Using wavelet transformation and a GM-ARMA model
to forecast stock index
WU Zhaoyang
(The Department of Mathematics and
Statistics,
Concordia
University,
Montreal H3G 2H9
,
Canada)
Abstract
�：
During the process of building a hybrid model by combining wavelet decomposition and other techniques，�
there is no standard in terms of selecting a wavelet base function and decomposition
level.
The commonly used ways
are usually based on the researcher's experience or several experiments instead of a quantitative approach. In addi-
tion
�，many
hybrid models based on wavelet decomposition do not consider the interaction between sub models. In-
stead of estimating the parameters in all sub models as the whole，they estimate the parameters separately，which
lead to that the prediction result is not optimal. In order to solve this problem，this paper first introduced two new
parameters，wavelet functions and decomposition levels，then quantitatively estimated all the parameters as a whole
for the purpose of building an optimal hybrid model. For convenience, the model was called the WGM-ARMA mod-
el because it combines the wavelet decomposition，grey model，as well as autoregressive integrated moving average
(ARMA) model. Experimental results show that the hybrid model significantly reduces prediction
errors.
As a re-
sult
�，it
can be concluded that the model in terms of forecasting stock index is valid and useful，along with the meth-
od used to construct the optimal hybrid model.
Keywords
�：
wavelet decomposition
�；
grey model
�；
ARMA model
�；
GM-ARMA model
�；
stock prediction
ARIMA�模型（autoregressive integrated moving
average model)和GM(
�1，1
�)模型作为应用广泛的时�
间序列模型，长期以来被许多学者用于股票价格序�
列的研究中
[15]
.由于这2种模型对于时间序列的�
预测各有侧重，因此一些学者提出了整合这2个模�
型的组合模型并称之为GM-ARMA模型（grey model
收稿日期:201(M)9-18.
通信作者：吴朝阳• E-mail�： hostingca@
gmail.
com.
and autoregressive integrated moving average mod-
el)
[6]
.但是GM-ARMA模型并不是一个最优的模�
型，因为子模型GM(1，1)模型没有经过优化，同时2�
个子模型在结合时，也没有考虑进行最佳的整合.为�
此笔者提出了改进的GM-ARMA模型以克服上述缺�
点并称为 RGM-ARMA( revised GM-ARMA)模型
[7]
，�
实例证明RGM-ARMA的预测误差小于单一模型和�
GM-ARMA�模型•
但是RGM-ARMA模型在预测误差上还是偏�
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