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May 2004 The tail of the stationary distribution of a random coefficient AR(q) model
Claudia Klüppelberg, Serguei Pergamenchtchikov
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Ann. Appl. Probab. 14(2): 971-1005 (May 2004). DOI: 10.1214/105051604000000189


We investigate a stationary random coefficient autoregressive process. Using renewal type arguments tailor-made for such processes, we show that the stationary distribution has a power-law tail. When the model is normal, we show that the model is in distribution equivalent to an autoregressive process with ARCH errors. Hence, we obtain the tail behavior of any such model of arbitrary order.


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Claudia Klüppelberg. Serguei Pergamenchtchikov. "The tail of the stationary distribution of a random coefficient AR(q) model." Ann. Appl. Probab. 14 (2) 971 - 1005, May 2004.


Published: May 2004
First available in Project Euclid: 23 April 2004

zbMATH: 1094.62114
MathSciNet: MR2052910
Digital Object Identifier: 10.1214/105051604000000189

Primary: 60H25 , 60J10
Secondary: 62P05 , 91B28 , 91B84

Keywords: ARCH model , autoregressive model , geometric ergodicity , heteroscedastic model , random coefficient autoregressive process , random recurrence equation , regular variation , renewal theorem for Markov chains , Strong mixing

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.14 • No. 2 • May 2004
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