We test the importance of multivariate information for modelling and forecasting inflation's conditional mean and variance. In the literature, the existence of inflation's conditional heteroskedasticity has been debated for years, as it seemed to appear only in some datasets and for some lag lengths. This phenomenon might be due to the fact that inflation depends on a linear combination of economy-wide dynamic common factors, some of which are conditionally heteroskedastic and some are not. Modelling the conditional heteroskedasticity of the common factors can thus improve the forecasts of inflation's conditional mean and variance. Moreover, it allows to detect and predict conditional correlations between inflation and other macroeconomic variables, correlations that might be exploited when planning monetary policies. A new model, the Dynamic Factor GARCH (DF-GARCH), is used here to exploit the relations between inflation and the other macroeconomic variables for inflation forecasting purposes. The DF-GARCH is a dynamic factor model with the additional assumption of conditionally heteroskedastic dynamic factors. When comparing the Dynamic Factor GARCH with univariate models and with the traditional dynamic factor models, the DF-GARCH is able to provide better forecasts both of inflation and of its conditional variance.