Nonlinear time series analysis and its application to flood forecasting

Abstract

We review nonlinear time series analysis based on embedding, especially time series prediction and its application to flood forecasting. When we apply the nonlinear time series analysis, we assume that observed time series are deterministically generated by a certain dynamical system, not by a probabilistic distribution.Although it seems difficult to estimate the original dynamical system, we can reconstruct an attractor of the original system based on embedding theorems. Using the reconstructed attractors, we can analyze the dynamics, e.g., detecting causality, predicting future states. In this article, we review classical methods to state-of-the art methods, and we also introduce our ongoing work.