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We present the Beta- t -QVAR (quasi-vector autoregression) model for the joint modelling of score-driven location plus scale of strictly stationary and ergodic variables. Beta- t -QVAR is an extension of Beta- t -EGARCH (exponential generalized autoregressive conditional heteroscedasticity) and Beta- t -EGARCH-M (Beta- t -EGARCH-in-mean). We prove the asymptotic properties of the maximum likelihood (ML) estimator for correctly specified Beta- t -QVAR models. We use Dow Jones Industrial Average (DJIA) data for the period of 1985–2020. We find that the volatility forecasting accuracy of Beta- t -QVAR is superior to the volatility forecasting accuracies of Beta- t -EGARCH, Beta- t -EGARCH-M, A-PARCH (asymmetric power ARCH), and GARCH for the period of 2010–2020.

Score-driven location plus scale models: asymptotic theory and an application to forecasting Dow Jones volatility