Determine why GINN-0 can outperform GARCH on out-of-sample volatility forecasting

Determine the mechanism by which the GINN-0 model—defined as the special case of the GARCH-Informed Neural Network with weight λ=0 that trains an LSTM to minimize mean squared error between its predicted daily log-return variance and the variance forecasted by a GARCH(1,1) model—can, in some stock index datasets, achieve higher out-of-sample volatility forecasting accuracy than the GARCH(1,1) model whose outputs it is trained to mimic.

Background

The paper introduces GARCH-Informed Neural Networks (GINN), a hybrid approach that combines a traditional GARCH model with an LSTM. Training uses a weighted loss that blends the mean squared error (MSE) to ground-truth variance with the MSE to the GARCH-predicted variance. The special case GINN-0 sets the weight λ to 0, so the network only minimizes the MSE between its variance predictions and those produced by the GARCH model, effectively learning to mimic the GARCH forecasts.

Empirically, across multiple stock index datasets, GINN-0 sometimes performs better out-of-sample than the GARCH model itself, despite not using ground-truth variance in its loss. The authors hypothesize that the LSTM component may act as additional regularization, producing smoother and potentially more generalizable predictions, but explicitly state that the reason for this superiority remains unclear.