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This paper presents a novel estimator of orthogonal GARCH models, whichcombines (eigenvalue and -vector) targeting estimation with stepwise(univariate) estimation. We denote this the spectral targeting estimator. Thistwo-step estimator is consistent under finite second order moments, whileasymptotic normality holds under finite fourth order moments. The estimator isespecially well suited for modelling larger portfolios: we compare theempirical performance of the spectral targeting estimator to that of the quasimaximum likelihood estimator for five portfolios of 25 assets. The spectraltargeting estimator dominates in terms of computational complexity, being up to57 times faster in estimation, while both estimators produce similarout-of-sample forecasts, indicating that the spectral targeting estimator iswell suited for high-dimensional empirical applications.

Spectral Targeting Estimation of $\lambda$-GARCH models