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USING SUBSPACE METHODS FOR ESTIMATING ARMA MODELS FOR MULTIVARIATE TIME SERIES WITH CONDITIONALLY HETEROSKEDASTIC INNOVATIONS

Published online by Cambridge University Press:  04 April 2008

Dietmar Bauer
Dietmar Bauer*
Affiliation:
arsenal research
*
Address correspondence to Dietmar Bauer, arsenal research, Giefingg. 2, A-1210 Vienna, Austria; e-mail: Dietmar.Bauer@arsenal.ac.at.
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Abstract

This paper deals with the estimation of linear dynamic models of the autoregressive moving average type for the conditional mean for stationary time series with conditionally heteroskedastic innovation process. Estimation is performed using a particular class of subspace methods that are known to have computational advantages as compared to estimation based on criterion minimization. These advantages are especially strong for high-dimensional time series. Conditions to ensure consistency and asymptotic normality of the subspace estimators are derived in this paper. Moreover asymptotic equivalence to quasi maximum likelihood estimators based on the Gaussian likelihood in terms of the asymptotic distribution is proved under mild assumptions on the innovations. Furthermore order estimation techniques are proposed and analyzed.

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 4 , August 2008 , pp. 1063 - 1092
Copyright
Copyright © Cambridge University Press 2008

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