Noise reduction and prediction of noisy time series
Liang-yue Cao
Institute of Theoretical Physics, Academia Sinica,
Beijing 100080, China
Almost all realistic time series contain noise. It certainly brings us many difficulties for characterizing and predicting them. Although many efforts have been devoted to the development of approaches to noisy time series analysis, for example, a lot of methods have been developed for noise reduction, there are still a number of open problems, for example, prediction. In this paper, our main work is prediction. Two approaches are used, one is to train a predictive model directly from noisy data and the other is to do it from the noise-reduced data. We compare these two approaches by testing short-term and long-term predictions on several artificial time series. On the other hand, we give a new method of noise reduction, which we call ``dynamical filter" and which is quite effective for the noisy time series from continuous-time systems even if the noise level is relatively high. We also compare our method with some others.