基于小波的回归-GARCH模型及其在外汇储备中的应用

结合小波变换、多项式回归和GARCH模型对中国的外汇储备进行分析及预测.首先利用db4小波对数据进行去噪处理,并对去噪后的数据建立多项式回归模型.由于去噪后的数据与回归模型之间存在残差,且残差具有自回归条件异方差效应,故对该残差建立GARCH模型.然后将回归模型和GARCH模型进行线性叠加,从而得到基于小波分析的回归-GARCH模型.最后将预测值与实际值进行拟合,发现拟合效果较好.充分证明了小波变换、多项式回归和GARCH模型相结合的方法在处理外汇储备这类具有明显增长趋势的非平稳时间序列时,具有明显的优越性,是一项有用的分析预测工具.

Wavelet-Based Regression-GARCH Model and Its Application in Foreign Exchange Reserves

The wavelet transform and the polynomial regression were combined with the GARCH model to analyze and forecast China's foreign exchange reserve.The data were de-noised by the db4 wavelet to establish polynomial regression model.Seeing that between the residuals of the de-noised data and the regression model there exist the auto regressive conditional heteroskedasticity (ARCH) effects, the GARCH model was created.Linear superposing the regression model and GARCH model, a regression-GARCH based on wavelet analysis was proposed.Comparing the predicted value and the actual value, it is found that the result in the paper is quite well.In other words, the method presented has obvious advantages and it's a useful predictive analysis tool in dealing with the non-stationary time series which has obvious growth trend just like foreign exchange reserves.