The Tail of the Stationary Distribution of a Random Coefficient AR(q) Model

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.