We extend recurrent neural networks to include several flexible timescales
for each dimension of their output, which mechanically improves their abilities
to account for processes with long memory or with highly disparate time scales.
We compare the ability of vanilla and extended long short term memory networks
(LSTMs) to predict asset price volatility, known to have a long memory.
Generally, the number of epochs needed to train extended LSTMs is divided by
two, while the variation of validation and test losses among models with the
same hyperparameters is much smaller. We also show that the model with the
smallest validation loss systemically outperforms rough volatility predictions
by about 20% when trained and tested on a dataset with multiple time series.

我们将循环神经网络扩展到包含几个灵活的时间尺度，这在机械上提高了它们对具有长期记忆或高度不同时间尺度进程的处理能力。通过比较普通和扩展的长短期记忆网络（LSTMs）在预测已知具有长期记忆的资产价格波动性方面的能力，我们发现扩展的 LSTMs 所需的训练时期减少了一半，而具有相同超参数的模型的验证和测试损失的变化要小得多。我们还展示了在多时间序列数据集上进行训练和测试时，验证损失最小的模型相对于粗略波动性预测的表现普遍提高了大约 20％。