  The high-frequency band of the $\delta^{18}\mbox{O}$ variations in the North
Greenland Ice Core Project displays fluctuation levels that increase as one
approaches the onset of an interstadial (warm) period. For some of the events
it is possible to establish statistical significance using Monte-Carlo
simulations with a non-parametric null model with random phases and the same
spectral density as the $\delta^{18}\mbox{O}$ record during the stadial
periods. Similar results are found for the locally estimated Hurst exponent for
the high-frequency fluctuations, and it is therefore natural to interpret these
findings as so-called "critical slowing down" signatures, i.e. early-warning
signs of tipping points. The observed "slowing down" is found to be similar
(and perhaps even stronger) in the Younger Dryas, suggesting that there are
some similarities between mechanisms of the Younger Dryas-Preboreal transition
and the onsets of the Greenland interstadials. It is also verified that the
temperature fluctuations during the last glacial period are characterized by
long-range dependence, where the stadial periods can be approximately modeled
as a $1/f$-noise. Persistent processes can take shape if the physical signal is
an aggregation of several different processes, where each process responds to
perturbations on a certain characteristic time scale. The results are
consistent with the hypothesis that both the onsets of the Greenland
interstadials and the Younger Dryas-Preboreal transition are caused by tipping
points in dynamical processes with characteristic time scale of the order of
decades, and that the variability of other processes on longer time scales mask
the early-warning signatures in the $\delta^{18}\mbox{O}$ signal.
