The Annals of Applied Probability

The tail of the stationary distribution of a random coefficient AR(q) model

Claudia Klüppelberg and Serguei Pergamenchtchikov

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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.

Article information

Ann. Appl. Probab., Volume 14, Number 2 (2004), 971-1005.

First available in Project Euclid: 23 April 2004

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Zentralblatt MATH identifier

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60H25: Random operators and equations [See also 47B80]
Secondary: 62P05: Applications to actuarial sciences and financial mathematics 91B28 91B84: Economic time series analysis [See also 62M10]

ARCH model autoregressive model geometric ergodicity heteroscedastic model random coefficient autoregressive process random recurrence equation regular variation renewal theorem for Markov chains strong mixing


Klüppelberg, Claudia; Pergamenchtchikov, Serguei. The tail of the stationary distribution of a random coefficient AR (q) model. Ann. Appl. Probab. 14 (2004), no. 2, 971--1005. doi:10.1214/105051604000000189.

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