  We develop methodology allowing to simulate a stationary functional time
series defined by means of its spectral density operators. Our framework is
general, in that it encompasses any such stationary functional time series,
whether linear or not. The methodology manifests particularly significant
computational gains if the spectral density operators are specified by means of
their eigendecomposition or as a filtering of white noise. In the special case
of linear processes, we determine the analytical expressions for the spectral
density operators of functional autoregressive (fractionally integrated) moving
average processes, and leverage these as part of our spectral approach, leading
to substantial improvements over time-domain simulation methods in some cases.
The methods are implemented as an R package (specsimfts) accompanied by several
demo files that are easy to modify and can be easily used by researchers aiming
to probe the finite-sample performance of their functional time series
methodology by means of simulation.
