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

2004/05/01 by Claudia Klüppelberg, Claudia Kluppelberg, Serguei Pergamenchtchikov · 2 citations
Economics, Econometrics and Finance · Mathematics · #Credit Risk and Financial Regulations #Financial Risk and Volatility Modeling #Stochastic processes and financial applications #math.PR #msc:60H25 #msc:60J10 #msc:62P05 #msc:91B28 #msc:91B84

paper · pdf · doi:10.1214/105051604000000189

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

openalex publication_date 2004/05/01 · arxiv created 2004/05/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Regular variation of GARCH processes
• Random difference equations and Renewal theory for products of random matrices

Cited by

• Hidden regular variation for stochastic recursions with diagonal matrices
• The Intrinsic Instability of Financial Markets

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