Abstract For large multivariate models of generalized autoregressive conditional heteroskedasticity (GARCH), it is important to reduce the number parameters cope with ‘curse dimensionality’. Recently, Laurent, Rombouts and Violante (2014 “Multivariate Rotated ARCH Models” Journal Econometrics 179 : 16–30) developed rotated GARCH model, which focuses on for standardized variables. This paper ext...