  We present a detailed analysis of the time series of time-stamped neutron
counts obtained by single-neutron interferometry. The neutron counting
statistics display the usual Poissonian behavior, but the variance of the
neutron counts does not. Instead, the variance is found to exhibit a dependence
on the phase-shifter setting which can be explained by a probabilistic model
that accounts for fluctuations of the phase shift. The time series of the
detection events exhibit long-time correlations with amplitudes that also
depend on the phase-shifter setting. These correlations appear as damped
oscillations with a period of about 2.8 s. By simulation, we show that the
correlations of the time differences observed in the experiment can be
reproduced by assuming that, for a fixed setting of the phase shifter, the
phase shift experienced by the neutrons varies periodically in time with a
period of 2.8 s. The same simulations also reproduce the behavior of the
variance. Our analysis of the experimental data suggests that time-stamped data
of singleparticle interference experiments may exhibit transient features that
require a description in terms of non-stationary processes, going beyond the
standard quantum model of independent random events.
