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Klüppelberg, Claudia and Pergamenchtchikov, S. (2002): The Tail of the Stationary Distribution of a Random Coefficient AR(q) Model. Collaborative Research Center 386, Discussion Paper 267
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Abstract

We investigate a stationary random cofficient 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 behaviour of any such model of arbitrary order.