Should You Use GARCH Models for Forecasting Volatility? A Comparison to GRU Neural Networks

The GARCH model is the most used technique for forecasting conditional volatility. However, the nearly integrated behaviour of the conditional variance originates from structural changes which are not accounted for by standard GARCH models. We compare the forecasting performance of the GARCH model to three regime switching models: namely, the Markov Switching GARCH, the Hidden Markov Model, and the Gated Recurrent Unit neural network. We define the number of optimal states by means of three methods: piecewise linear regression, Baum–Welch algorithm and Markov Chain Monte Carlo. Since forecasting volatility models face the bias-variance trade-off, we compare their out-of-sample forecasting performance via a walk-forward methodology. Moreover, we provide a robustness check for the results by applying k-fold cross-validation to the original time series. The Gated Recurrent Unit network is the best suited for volatility forecasting, while the Hidden Markov Model is the best at discerning the market regimes.