Long Strange Segments, Ruin Probabilities and the Effect of Memory on Moving Average Processes

Details Long Strange Segments, Ruin Probabilities and the Effect of Memory on Moving Average Processes Long Strange Segments, Ruin Probabilities and the Effect of Memory on Moving Average Processes

2010-02-14

arxiv.org/abs/1002.2751v2

Stochastic Processes and their Applications, 120 (2010), 2302-2330

Mathematics

Probability

29 pages, minor changes and a few typo correction from last version

Scientific paper

10.1016/j.spa.2010.08.004

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.

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