对比传统模型与深度学习，发现不同数据粒度下各有优劣。
COMEX Copper Futures Volatility Forecasting: Econometric Models and Deep Learning
- 用HAR和RNN类模型预测铜期货波动率，分日频与小时频测试
- 日频下HAR最优，小时频下深度学习超越GARCH模型
- 长周期预测中深度学习性能逐步逼近传统模型
本文研究了在不同高频区间下，基于经济计量模型与深度学习循环神经网络对COMEX铜期货实际波动率的预测表现。所考察的经济计量模型包括GARCH与HAR，深度学习模型则涵盖RNN、LSTM与GRU。在滚动窗口法预测铜期货日频实际波动率时，经济计量模型整体优于循环神经网络，其中HAR取得最低QLIKE损失值。然而，当数据替换为小时级高频实际波动率后，深度学习模型超越GARCH模型，HAR的QLIKE损失值也达到可比水平。尽管机器学习模型存在黑箱特性，其在高频率数据下仍表现出更优的预测性能，且在日频预测中随着预测时滞延长，深度学习模型在部分损失函数指标上逐渐缩小与GARCH模型的差距。总体而言，对于铜期货的日频波动率预测，HAR模型仍为最优选择。
原文摘要 · Abstract (English)
This paper investigates the forecasting performance of COMEX copper futures realized volatility across various high-frequency intervals using both econometric volatility models and deep learning recurrent neural network models. The econometric models considered are GARCH and HAR, while the deep learning models include RNN (Recurrent Neural Network), LSTM (Long Short-Term Memory), and GRU (Gated Recurrent Unit). In forecasting daily realized volatility for COMEX copper futures with a rolling window approach, the econometric models, particularly HAR, outperform recurrent neural networks overall, with HAR achieving the lowest QLIKE loss function value. However, when the data is replaced with hourly high-frequency realized volatility, the deep learning models outperform the GARCH model, and HAR attains a comparable QLIKE loss function value. Despite the black-box nature of machine learning models, the deep learning models demonstrate superior forecasting performance, surpassing the fixed QLIKE value of HAR in the experiment. Moreover, as the forecast horizon extends for daily realized volatility, deep learning models gradually close the performance gap with the GARCH model in certain loss function metrics. Nonetheless, HAR remains the most effective model overall for daily realized volatility forecasting in copper futures.
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