基于小波方差分解的混沌时间序列噪声估计和阈值去噪

针对小波噪声处理时重视信号的分解而忽略噪声特性的问题,利用小波变换的方差分解功能对白噪声的小波系数方差进行分析,提出一种新的小波噪声估计和阈值去噪方法。该方法以时间序列第一、二层的小波方差来估计噪声水平,通过计算出噪声方差在各层小波系数上的分布来确定软阈值。对Lorenz、Chen等混沌系统的仿真结果表明,该方法有较好的效果。其后对上证指数和上海天然胶期货日收盘价序列进行去噪处理,验证了该方法的有效性。

Noise estimation and reduction for chaotic time series by wavelet variance decomposition

In wavelet noise processing, signal decomposition catches more attention while noise itself is ignored. To solve this problem, by using the function of wavelet variance decomposition to analyze white noise, a new method of noise estimation and reduction by thresholding was proposed for chaotic time series. The noise level was estimated with wavelet variances at first and second scale, while the soft threshold was chosen by calculating wavelet variance of noise at every scale. The method was tested in Lorenz and Chen's system. The result shows that the proposed method is better than other wavelet noise estimation and reduction methods. At last, it is proved to be effective in de-noising Shanghai Stock Exchange (SSE) index and Shanghai Futures Exchange (SHFE) rubber futures time series.