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

摘要

This paper deals with the estimation of linear dynamic models of the autoregres-sive moving average type forsthe 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.