Asymptotic p-value upper bounds converge on the LSA density. Notice that the p-value upper bound (red) converges in the tail to the approximate LSA density (blue), an attractive quality. As the number of time steps (n) increase, both the density and the p-value upper bound push up against zero. This is similar to the asymptotic behaviour of PCC.
Durno et al. BMC Genomics 2013 14(Suppl 1):S3 doi:10.1186/1471-2164-14-S1-S3