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.
"The tail of the stationary distribution of a random coefficient AR(q) model." Ann. Appl. Probab. 14 (2) 971 - 1005, May 2004. https://doi.org/10.1214/105051604000000189