  We anticipate noise from the Laser Interferometer Space Antenna (LISA) will
exhibit nonstationarities throughout the duration of its mission due to factors
such as antenna repointing, cyclostationarities from spacecraft motion, and
glitches as highlighted by LISA Pathfinder. In this paper, we use a surrogate
data approach to test the stationarity of a time series which does not rely on
the Gaussianity assumption. The main goal is to identify noise
nonstationarities in the future LISA mission. This will be necessary for
determining how often the LISA noise power spectral density (PSD) will need to
be updated for parameter estimation routines. We conduct a thorough simulation
study illustrating the power/size of various versions of the hypothesis tests,
and then apply these approaches to differential acceleration measurements from
LISA Pathfinder. We also develop a data analysis strategy for addressing
nonstationarities in the LISA PSD, where we update the noise PSD over time,
while simultaneously conducting parameter estimation, with a focus on planned
data gaps.
