and
k
r
is asymptotically normally distributed under the assumption of weak stationarity. The 95%
confidence limits for the correlogram can therefore be plotted at
1 / 2 N N , and are often
further approximated to 0
2 N
. Thus, for example, if a series has length 100, the
approximate 95% confidence band is
2 1 0 0 0 .2 0
. Any given
k
r
has a 5% chance of being
outside the 95% confidence limits, so that one value outside the limits might be expected in a
correlogram plotted out to lag 20 even if the time series is drawn from a random (not
autocorrelated) population.