A Topological View of Chaos : (II) Independence and Noise Cancellation
Kim Hung Soo, Yoon Yong Nam · Journal of the Korean Society of Civil Engineers · 1996
Since autocorrelation function cannot distinguish chaotic system from random noise, we apply the power spectrum for some time series to see if the power spectrum can discern between chaotic system and random process. In our experiment. the chaotic system and the random process shows the same structure as broad band spectra. Therefore, the power spectrum cannot also distinguish chaotic time series from random signal. In step two, the histogram of close returns plot is used for testing independence of a daily streamflow at Cache La Poudre river. The result shows its periodicity as proved by close returns plot (Kim and Yoon, this issue). This also exhibits the daily streamflow should be interpreted by some periodic stochastic models. In final step, we show the noise of time series can be reduced by using the simple moving average method on the close returns plot. An example of a periodic time series is explained for the noise reduction and the result represents that the moving average technique is useful for the noise cancellation.