Real-Time Forecast of DSGE Models with Time-Varying Volatility in GARCH Form

Recent research shows that time-varying volatility plays a crucial role in nonlinear modeling. Contributing to this literature, we suggest a DSGE-GARCH approach that allows for straightforward computation of DSGE models with time-varying volatility, where the volatility component is formulated as a GARCH process. As an applica- tion of our approach, we examine the forecasting performance of the DSGE-GARCH model using euro area real-time data. Our findings suggest that the DSGE-GARCH approach is superior in out-of-sample forecasting performance in comparison to various other benchmarks for the forecast of inflation rates, output growth and interest rates, especially in the short term. Comparing our approach to the widely used stochastic volatility specification using in-sample forecasts, we also show that the DSGE-GARCH is superior in in-sample forecast quality and computational efficiency. In addition to these results, our approach reveals interesting properties and dynamics of time-varying correlations (conditional correlations)