  We show that a time series $x_t$ evolving by a non-local update rule $x_t = f
(x_{t-n},x_{t-k})$ with two different delays $k<n$ can be mapped onto a local
process in two dimensions with special time-delayed boundary conditions
provided that $n$ and $k$ are coprime. For certain stochastic update rules
exhibiting a non-equilibrium phase transition this mapping implies that the
critical behavior does not depend on the short delay $k$. In these cases, the
autocorrelation function of the time series is related to the critical
properties of directed percolation.
