Abstract
Real systems are often composed of many elements interacting with each other and show complex behavior. To predict these complex systems, we can refer to their past behavior, but all of the observed elements do not always compose the same system. Thus, we must detect some essential elements from the observed elements so as to improve the prediction accuracy of learning data. Moreover, if we apply Takens's embedding theorem to reconstruct an attractor with only a single element, we need not select elements, but we must optimize embedding parameters. In any case, because we must solve the above optimization problems, we applied the genetic algorithm (GA) as an example of metaheuristic techniques. Moreover, real systems might be nonstationary and their own mechanism changes dynamically. Therefore, we reiterated the GA for each optimization with simple algorithms to embed and to predict time-series data to save numerical costs. Through some simulations, we confirmed that our dynamical optimization can improve the prediction accuracy of multivariate nonlinear systems, even financial markets, and can help us to examine whether the structure of a complex system dynamically changes or not.
