We propose a new class of financial volatility models, called the REcurrent Conditional Heteroskedastic (RECH) models, to improve both in-sample analysis and out-of-sample forecasting of the traditional conditional heteroskedastic models. In particular, we incorporate auxiliary deterministic processes, governed by recurrent neural networks, into the conditional variance of the traditional conditional heteroskedastic models, for example, GARCH-type models, to flexibly capture the dynamics of the underlying volatility. RECH models can detect interesting effects in financial volatility overlooked by the existing conditional heteroskedastic models such as the GARCH, GJR, and EGARCH. The new models often have good out-of-sample forecasts while still explaining well the stylized facts of financial volatility by retaining the well-established features of econometric GARCH-type models. These properties are illustrated through simulation studies and applications to 31 stock indices and exchange rate data. An user-friendly software package, together with the examples reported in the paper, is available at https://github.com/vbayeslab.
