Long strange segments, ruin probabilities and the effect of memory on moving average processes
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 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.
NSA grant MSPF-05G-049, ARO grant W911NF-07-1-0078 and NSF training grant ``Graduate and Postdoctoral Training in Probability and Its Applications''
ruin probability; long strange segments; moving average; long range dependence; long memory