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

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

2004-05-14

arxiv.org/abs/math/0405297v1

Annals of Applied Probability 2004, Vol. 14, No. 2, 971-1005

Mathematics

Probability

Scientific paper

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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