The distribution of the maximum of a first-order moving average: The discrete casex

Extreme value theory for discrete observations is very much underdeveloped. Here, we derive exact expressions for the cumulative distribution function of M-n, the maximum of a sequence of n discrete observations from a moving average of order one. A solution appropriate for large n takes the form P-r (M-n <= x) = Sigma(j=1)' beta(jx) nu(n)(jx), where {nu(jx)} are the eigenvalues of a certain matrix, and I depends on the number of possible values of the underlying random variables.