Delay-embedding is well-known for time-series analysis to reconstruct original dynamics. Takens' theorem ensures validity of the delay-embedding, nevertheless configuration of embedded data may easily vary with the delay width and the delay dimension, namely, “way of embedding”. In this talk, we investigate a mathematical structure of the framework of delay-embedding analysis in view of the integral operator theory, in order to provide Ansatz for the appropriate way of embedding. Moreover, we construct a prediction model and its predictability estimates by the use of this method. Some practical studies based on this methodology will be also shown.
(This talk will be given in Japanese.)