If a time series is completely random, and the sample size is
large, the lagged-correlation coefficient is approximately normally distributed with mean 0 and
variance 1/N (Chatfield 2004). It follows that the approximate threshold, or critical, level of
correlation for 95% significance
( 0 .0 5)
is
.9 5 r N 0 2 /
, where
N
is the sample size.
Accordingly, the required level of correlation for “significance” becomes very small at large
sample size (Figure 3.3).