The study aimed at determining a set of superior generalized orthogonal-GARCH (GO-GARCH) models for forecasting time-varying conditional correlations and variances of five foreign exchange rates vis-à-vis the Nigerian Naira. Daily data covering the period 02/01/2009 to 19/03/2015 was used, and four estimators of the GO-GARCH model were considered for fitting the models. Forecast performance tests were conducted using the Diebold-Mariano (DM) and the model confidence set (MCS) tests procedures. The DM test indicates preference for the GO-GARCH model estimated with nonlinear least squares (NLS) estimator - denoted as GOGARCH-NLS, while the MCS test determined a set of superior models (SSM) which comprised of GO-GARCH-NLS and GOGARH model estimated by the method-of-moment, denoted as GO-GARCH-MM. These models were deemed best and adequate for forecasting of the five exchange rate dynamics.