The paper presents an approach to modelling and forecasting the Industrial Production Index which allows to account for the presence of asymmetric effects in both the conditional mean and the conditional variance. More precisely, the proposed approach combines a Self Exciting Threshold AutoRegressive (SE- TAR) model for the conditional mean with a conditional heteroskedastic model fitted to the residuals. Namely, we use a Constrained Changing Parameters Volatility (CPV-C) model which allows to capture asymmetries in the conditional variance dynamics by means of interaction terms between past shocks and volatilities. The out of sample fitting performance of the model is evaluated by means of an application to a time series of U.S. data.