Delay embedding in the presence of dynamical noise

Abstract

We present a new embedding theorem for time series, in the spirit of Takens's theorem, but requiring multivariate signals. Our result is part of a growing body of work that extends the domain of geometric time series analysis to some genuinely stochastic systems - including such natural examples as xj+1 = φ(xj) + ηj where φ is some fixed map and the ηj are i.i.d. random displacements.