Open Access
August 2002 Processes with long memory: Regenerative construction and perfect simulation
Francis Comets, Roberto Fernández, Pablo A. Ferrari
Ann. Appl. Probab. 12(3): 921-943 (August 2002). DOI: 10.1214/aoap/1031863175


We present a perfect simulation algorithm for stationary processes indexed by $\mathbb{Z}$, 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, Martínez 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 Fernández. Pablo A. Ferrari. "Processes with long memory: Regenerative construction and perfect simulation." Ann. Appl. Probab. 12 (3) 921 - 943, August 2002.


Published: August 2002
First available in Project Euclid: 12 September 2002

zbMATH: 1016.60061
MathSciNet: MR1925446
Digital Object Identifier: 10.1214/aoap/1031863175

Primary: 60G99
Secondary: 60K10 , 62J02 , 68U20

Keywords: binary autoregressions , chains with complete connections , perfect simulation , regeneration

Rights: Copyright © 2002 Institute of Mathematical Statistics

Vol.12 • No. 3 • August 2002
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