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A central limit theorem for random coefficient autoregressive models and ARCH/GARCH models

Part of: Markov processes

Published online by Cambridge University Press:  01 July 2016

Andreas Rudolph
Andreas Rudolph*
Affiliation:
IBM
*
∗ Postal address: IBM WT WZH, Vangerowstr. 18, 69115 Heidelberg, Germany.
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Abstract

In this paper we study the so-called random coeffiecient autoregressive models (RCA models) and (generalized) autoregressive models with conditional heteroscedasticity (ARCH/GARCH models). Both models can be represented as random systems with complete connections. Within this framework we are led (under certain conditions) to CL-regular Markov processes and we will give conditions under which (i) asymptotic stationarity, (ii) a law of large numbers and (iii) a central limit theorem can be shown for the corresponding models.

Keywords

RCA modelsARCH/GARCH modelsrandom systems with complete connectionsmarkov processesCL regularitylaw of large numbersasymptotic stationarity

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 30 , Issue 1 , March 1998 , pp. 113 - 121
Copyright
Copyright © Applied Probability Trust 1998 

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