Processes with Long Memory: Regenerative Construction and Perfect Simulation

Details Processes with Long Memory: Regenerative Construction and Perfect Simulation Processes with Long Memory: Regenerative Construction and Perfect Simulation

2000-09-22

arxiv.org/abs/math/0009204v3

Ann. Appl. Probab. Volume 12, Number 3 (2002), 921-943

Mathematics

Probability

27 pages, one figure. Version accepted by Annals of Applied Probability. Small changes with respect to version 2

Scientific paper

10.1214/aoap/1031863175

We present a perfect simulation algorithm for stationary processes indexed by Z, with summable memory decay. Depending on the decay, we construct the process on finite or semi-infinite intervals, explicitly from an i.i.d. uniform sequence. Even though the process has infinite memory, its value at time 0 depends only on a finite, but random, number of these uniform variables. The algorithm is based on a recent regenerative construction of these measures by Ferrari, Maass, Mart{\'\i}nez and Ney. As applications, we discuss the perfect simulation of binary autoregressions and Markov chains on the unit interval.

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