The tail of the stationary distribution of a random coefficient AR(q) model
Claudia Klüppelberg and Serguei Pergamenchtchikov
Source: Ann. Appl. Probab. Volume 14, Number 2
(2004), 971-1005.
Abstract
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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Keywords: ARCH model; autoregressive model; geometric ergodicity; heteroscedastic model; random coefficient autoregressive process; random recurrence equation; regular variation; renewal theorem for Markov chains; strong mixing
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Permanent link to this document: http://projecteuclid.org/euclid.aoap/1082737119
Digital Object Identifier: doi:10.1214/105051604000000189
Mathematical Reviews number (MathSciNet): MR2052910
Zentralblatt MATH identifier: 1094.62114
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