In the last few decades, a broad strand of literature in finance has implemented artificial neural networks as forecasting method. The major advantage of this approach is the possibility to approximate any linear and nonlinear behaviors without knowing the structure of the data generating process. This makes it suitable for forecasting time series which exhibit long memory and nonlinear dependencies, like conditional volatility. In this paper, I compare the predictive performance of feed-forward and recurrent neural networks (RNN), particularly focusing on the recently developed Long short-term memory (LSTM) network and NARX network, with traditional econometric approaches. The results show that recurrent neural networks are able to outperform all the traditional econometric methods. Additionally, capturing long-range dependence through Long short-term memory and NARX models seems to improve the forecasting accuracy also in a highly volatile framework.

中文翻译：

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用神经网络实现波动率预测

在过去的几十年中，金融领域的大量文献已将人工神经网络用作预测方法。这种方法的主要优点是可以在不知道数据生成过程结构的情况下近似任何线性和非线性行为。这使其适合于预测具有较长记忆和非线性相关性（例如条件波动）的时间序列。在本文中，我将前馈和递归神经网络（RNN）的预测性能进行了比较，特别是将其与传统的计量经济学方法集中在最近开发的长短期记忆（LSTM）网络和NARX网络上。结果表明，递归神经网络能够胜过所有传统的计量经济学方法。另外，