Using Subspace Methods for Estimating ARMA Models for Multivariate Time Series with Conditionally Heteroskedastic Innovations

Dietmar Bauer ()

No 1452, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This paper deals with the estimation of linear dynamic models of the ARMA type for the conditional mean for time series with conditionally heteroskedastic innovation process widely used in modelling financial time series. Estimation is performed using subspace methods which are known to have computational advantages as compared to prediction error methods based on criterion minimization. These advantages are especially strong for high dimensional time series. The subspace methods are shown to provide consistent estimators. Moreover asymptotic equivalence to prediction error estimators in terms of the asymptotic variance is proved. Also order estimation techniques are proposed and analyzed. The estimators are not efficient as they do not model the conditional variance. Nevertheless, they can be used to obtain consistent estimators of the innovations. In a second step these estimated residuals can be used in order to levitate the problem of specifying the variance model in particular in the multi-output case. This is demonstrated in an ARCH setting, where it is proved that the estimated innovations can be used in place of the true innovations for testing in a linear least squares context in order to specify the structure of the ARCH model without changing the asymptotic distribution.

Keywords: Multivariate models; conditional heteroskedasticity; ARMA systems; subspace methods (search for similar items in EconPapers)
JEL-codes: C13 C32 (search for similar items in EconPapers)
Pages: 33 pages
Date: 2004-02
New Economics Papers: this item is included in nep-ets and nep-fin
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Related works:
Journal Article: USING SUBSPACE METHODS FOR ESTIMATING ARMA MODELS FOR MULTIVARIATE TIME SERIES WITH CONDITIONALLY HETEROSKEDASTIC INNOVATIONS (2008)
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