The Tail of the Stationary Distribution of a Random Coefficient AR(q) Model

Klüppelberg, Claudia und Pergamenchtchikov, S. (2002): The Tail of the Stationary Distribution of a Random Coefficient AR(q) Model. Sonderforschungsbereich 386, Discussion Paper 267

Abstract

We investigate a stationary random cofficient 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 behaviour of any such model of arbitrary order.

• Dokumententyp: Paper
• Keywords: ARCH model, autoregressive model, geometric ergodicity, heteroscedastic model, random coeËcient autoregressive process, random recurrence equation, regular variation, renewal theorem for Markov chains, strong mixing
• Fakultät: Mathematik, Informatik und Statistik > Statistik > Sonderforschungsbereich 386 ; Sonderforschungsbereiche > Sonderforschungsbereich 386
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• Sprache: Englisch