非平稳时间序列循环行为的多分辨率分析表征与建模
Characterizing and modeling cyclic behavior in non-stationary time series through multi-resolution analysis
摘要：
提出了一种基于小波变换和遗传规划的非平稳时间序列多尺度变化特征描述和建模方法。循环变化，提取的小波和三次样条平滑，以及捕获的形式的动力学方程的遗传编程。为了说明的目的，我们分析了两个不同的非平稳金融时间序列，S&P CNX Nifty收盘指数的国家证券交易所（印度）和道琼斯工业平均指数收盘值通过Haar，Daubechies-4和连续Morlet小波研究在不同尺度上的波动特征，然后通过GP建模的周期性行为。周期变化出现在中间的时间尺度和相应的动力学方程揭示在不同尺度的特征行为。
英文摘要：
A method based on wavelet transform and genetic programming is proposed for characterizing and modeling variations at multiple scales in non-stationary time series. The cyclic variations, extracted by wavelets and smoothened by cubic splines, are well captured by genetic programming in the form of dynamical equations. For the purpose of illustration, we analyze two different non-stationary financial time series, S&P CNX Nifty closing index of the National Stock Exchange (India) and Dow Jones industrial average closing values through Haar, Daubechies-4 and continuous Morlet wavelets for studying the character of fluctuations at different scales, before modeling the cyclic behavior through GP. Cyclic variations emerge at intermediate time scales and the corresponding dynamical equations reveal characteristic behavior at different scales.
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