  This paper presents a novel estimator of orthogonal GARCH models, which
combines (eigenvalue and -vector) targeting estimation with stepwise
(univariate) estimation. We denote this the spectral targeting estimator. This
two-step estimator is consistent under finite second order moments, while
asymptotic normality holds under finite fourth order moments. The estimator is
especially well suited for modelling larger portfolios: we compare the
empirical performance of the spectral targeting estimator to that of the quasi
maximum likelihood estimator for five portfolios of 25 assets. The spectral
targeting estimator dominates in terms of computational complexity, being up to
57 times faster in estimation, while both estimators produce similar
out-of-sample forecasts, indicating that the spectral targeting estimator is
well suited for high-dimensional empirical applications.
