The Tail of the Stationary Distribution of an Autoregressive Process with Arch(1) Errors

where � enn∈ are i.i.d. random variables. Under general and tractable assumptions we show the existence and uniqueness of a stationary dis- tribution. We prove that the stationary distribution has a Pareto-like tail with a well-specified tail index which depends on α� λ and the distribution of the innovations � enn∈. This paper generalizes results for the ARCH(1) process (the case α = 0). The generalization requires a new method of proof and we invoke a Tauberian theorem.

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