  We propose a new class of financial volatility models, called the REcurrent
Conditional Heteroskedastic (RECH) models, to improve both in-sample analysis
and out-ofsample 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, e.g. 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 thirty-one stock indices and
exchange rate data. . An user-friendly software package together with the
examples reported in the paper are available at https://github.com/vbayeslab.
