A Nonlinear Dynamical System Approach for Analyzing Time Series with Event Size and Event Timing Information and its Applications

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In the proposed framework, first we assume an existence of an event dynamical system, which produces observed complex event time series. Thus, the important and essential information of the dynamical system is not only event sizes or event timings but both of observed event sizes and timings.To analyze several time series with complex behavior under our modeling framework, we evaluate prediction accuracy of event series using both the proposed method and the conventional method. For the evaluation, we use artificial event series generated from a mathematical model. As results, we show that the proposed framework is applicable for predicting event series. Then, we apply the proposed method to real world complex phenomena. We use experimental time series of a laser diode-pumped Nd:YVO_4 microchip laser, as one of the examples of possible chaotic phenomena. From this system, we can observe a single longitudinal mode oscillation at weak pumping power, whose output looks like spike oscillat … More ion. The proposed method is used for predicting the spike sizes and timings. We show that the proposed method is more effective for event prediction than the conventional methods, in such real world complex phenomena.As applications of our proposed scheme, first we apply the proposed method to predict the timings of occurrence of maxima of continuous time series. Here, maximum sizes and timings are treated as an output set of event sizes and timings, respectively. Then, we predict maxima of continuous time series produced from mathematical models and maxima of real world complex phenomena. Results of the proposed method show high accuracies of maxima prediction. Next we use the maximum prediction by the proposed method for improving long-term predictability of the observed continuous time series. Since it is widely acknowledged that one of the characteristics of deterministic chaos is long-term unpredictability, it is very interesting and important issue to remove long-term predictability of the continuous time series. Although we can take several strategies for realizing the long-term predictability, we use a simple method : we predict two successive maxima of the continuous time series, then we interpolate the values between these maxima. As results, we show that our modeling method is applicable for improving long-term prediction of the continuous time series. Less