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Processes with Long Memory: Regenerative Construction and Perfect Simulation

Francis Comets·Roberto Fernandez·Pablo A. Ferrari
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Abstract

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{\'ı}nez and Ney. As applications, we discuss the perfect simulation of binary autoregressions and Markov chains on the unit interval.

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Francis Comets, Roberto Fernandez, Pablo A. Ferrari. 2001-12-14. Processes with Long Memory: Regenerative Construction and Perfect Simulation. https://doi.org/10.1214/aoap%2F1031863175

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