基于小波的非平稳时间序列预测方法研究

摘要

According to the theory of wavelet analysis, a non-stationary time series forecasting method which is based on wavelet is put forward. Through the wavelet decomposition and single reconstruction, the original non-stationary time series is decomposed into a layer of approximation coefficients and several layers of detail coefficients. In the next step, each layer of coefficients is used to model and forecast, using the Auto-Regressive and Moving Average(ARMA)model once, and the BP neural network model once. After integrating layers of coefficients, the predictive value of the original time series is obtained. The result of the experiment, in which the network traffic data of internet nodes and daily maximum temperature data is used to model and forecast, demonstrates good accuracy of the method mentioned above. And it also shows that the prediction accuracy and curve fitting of the model using the BP neural network are better, which means that this model can be applied to the analysis and forecasting of non-stationary time series.%基于小波分析技术，将原始非平稳时间序列分解为一层近似系数和多层细节系数，对其分别采用自回归滑动平均模型以及BP神经网络模型，对各层系数进行建模与预测；通过整合各层系数，得到原始时间序列的预测值。运用这种方法对因特网某节点网络流量数据和某地区日最高气温数据进行预测的结果表明，建立在小波分解基础上的这两种方法都能够有效地应用于非平稳时间序列的预测；而小波-BP神经网络的预测方法无论是精度还是计算复杂度方面都要明显优于小波-ARMA方法。