  We obtain the rate of growth of long strange segments and the rate of decay
of infinite horizon ruin probabilities for a class of infinite moving average
processes with exponentially light tails. The rates are computed explicitly. We
show that the rates are very similar to those of an i.i.d. process as long as
the moving average coefficients decay fast enough. If they do not, then the
rates are significantly different. This demonstrates the change in the length
of memory in a moving average process associated with certain changes in the
rate of decay of the coefficients.
