Spectral Targeting Estimation of $λ$-GARCH models

Abstract

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.