New embedding technique for estimating the delay

Abstract

It has been reported that the chaos attractor generated from a differential equation containing a delay often attains a high dimension. When the high-dimensional time series data generated from a system containing a delay are analyzed, it is expected that the orbital reconstruction by the Takens embedding theorem is practically difficult. An approximate low-dimensional orbital reconstruction taking into account the delay is needed. However, when time series data containing a delay are treated, it is important to first estimate the delay accurately. Several methods have been proposed for estimating the delay. The previous methods are either those that cannot accurately estimate the delay while the existence of the delay can be recognized or those that can be applied only under the assumption that all state variables are observable. In this paper, a new embedding method and an algorithm are proposed for estimating the delay from an observed time series data set. By simulation, accurate estimation of the delay is confirmed. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(10): 10–16, 2000