  A scan statistic is examined for the purpose of testing the existence of a
global peak in a random process with dependent variables of any distribution.
The scan statistic tail probability is obtained based on the covariance of the
moving sums process, thereby accounting for the spatial nature of the data as
well as the size of the searching window. Exact formulas linking this
covariance to the window size and the correlation coefficient are developed
under general, common and auto covariance structures of the variables in the
original process. The implementation and applicability of the formulas are
demonstrated on families of multiple processes of t-statistics. A sensitivity
analysis provides further insight into the variant interaction of the tail
probability with the influence parameters. An R code for the tail probability
computation is offered within the supplementary material.
