Recent research shows that time-varying volatility plays a crucial role in non-linear modeling. Contributing to this literature, we suggest an 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 application of our approach, we examine the forecasting performance of this 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).

中文翻译：

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GARCH形式的时变波动率DSGE模型的实时预测

最近的研究表明，时变波动性在非线性建模中起着至关重要的作用。在这篇文献中，我们提出了一种方法，可以直接计算具有时变波动性的 DSGE 模型，其中波动性分量被公式化为 GARCH 过程。作为我们方法的应用，我们使用欧元区实时数据检查了 DSGE-GARCH 模型的预测性能。我们的研究结果表明，与其他各种通胀率、产出增长和利率预测基准相比，DSGE-GARCH 方法在样本外预测性能方面表现出色，尤其是在短期内。将我们的方法与使用样本内预测的广泛使用的随机波动率规范进行比较，我们还表明 DSGE-GARCH 在样本内预测质量和计算效率方面具有优越性。除了这些结果之外，我们的方法还揭示了时变相关性（条件相关性）的有趣属性和动态。