基于小波分析的ARMA-GARCH模型在金融时间序列中的应用

Application of ARMA-GARCH Model in Financial Time Series Based on Wavelet Analysis

利用小波分析方法对上证日综合指数收盘价序列进行分解与单支重构,得到低频序列和高频序列;然后根据各序列是否具有自回归条件异方差(ARCH)效应,建立相应的自回归移动平均(ARMA)模型或者ARMA-GARCH模型.最后将各子序列所建的模型进行线性组合,得到基于小波分析的ARMA-GARCH模型,并与直接用原始序列建立的模型作对比.最后比较试验结果发现,该模型的预测相对误差更小,从而说明该模型的可行性.

Firstly, the low-frquency sequences and high-frequency sequences of daily closing price of Shanghai Composite Index are got by using single signal decomposition and reconstruction with wavelet methods. Secondly, according to whether the sequences have the auto regressive conditional het- erokedasticity （ARCH） effects or not,the auto regressive moving average model（ARMA） or ARMA- GARCH model is created. Thirdly, the final model based on wavelet analysis is gained through a linear superposition of the models which have been established by the above sequences. By comparing the proposed prediction model with the original prediction model, the results indicate that the proposed prediction model based on wavelet analysis gives smaller relative errors and show that this method is effective and reasonable.