Despite the impressive success of deep neural networks in many application areas, neural network models have so far not been widely adopted in the context of volatility forecasting. In this work, we aim to bridge the conceptual gap between established time series approaches, such as the Heterogeneous Autoregressive (HAR) model, and state-of-the-art deep neural network models. The newly introduced HARNet is based on a hierarchy of dilated convolutional layers, which facilitates an exponential growth of the receptive field of the model in the number of model parameters. HARNets allow for an explicit initialization scheme such that before optimization, a HARNet yields identical predictions as the respective baseline HAR model. Particularly when considering the QLIKE error as a loss function, we find that this approach significantly stabilizes the optimization of HARNets. We evaluate the performance of HARNets with respect to three different stock market indexes. Based on this evaluation, we formulate clear guidelines for the optimization of HARNets and show that HARNets can substantially improve upon the forecasting accuracy of their respective HAR baseline models. In a qualitative analysis of the filter weights learnt by a HARNet, we report clear patterns regarding the predictive power of past information. Among information from the previous week, yesterday and the day before, yesterday's volatility makes by far the most contribution to today's realized volatility forecast. Moroever, within the previous month, the importance of single weeks diminishes almost linearly when moving further into the past.
翻译:尽管在许多应用领域深层神经网络取得了令人印象深刻的成功,但神经网络模型迄今尚未在波动预测的背景下得到广泛采用。在这项工作中,我们的目标是弥合既定的时间序列方法(如超异自动回归模型(HAR)模型)与最先进的深神经网络模型(HARNet)之间的概念差距。新推出的HARNet是基于一个分层的分层结构,它有助于模型参数数目中可接受模型领域的快速增长。HARNet可以允许一个明确的初始化计划,在优化之前,HARNet产生与相应的基准HAR模型几乎相同的预测。特别是在将QLIKE错误视为损失函数时,我们发现这一方法大大稳定了HARNet的最佳性。我们根据三个不同的股票市场指数评估了HARNet的绩效。根据这一评估,我们为模型的优化制定了明确的准则,并表明HARNet能够大大改进其各自基准模型预测的准确性,在优化之前,HARNet的几乎具有相同的预测重要性。在前一周内,通过对过去的信息进行定性分析,从以往的预测到前一周的预测,从头一周,从头一周,从头一周,从头一周,从头一周,从头一周,从头一周,从头一周,从头一周,从一个预测到头一周,从头一周,从头一周,从一个预测到头一周,从一个预测到头一周,从头一周,从头一周,从头一周,从质量分析到头一周,从头一周,从头一周,从头一周,从一个预测到头,从一个预测到尾,从头一周,从头一周,从头一周,从一个预测,从一个预测,从一个预测,从一个深度,从一个质量,从一个质量,从一个预测到头,从头,从头,从头,从头,从头,从头,从头,从头,从头,从头,从头,从头,从头,从头,从头,从头,从头,从头,从头,从头,从一个预测,从头,从头,从头,从头,从头,从头,从头,从头,从头,从头,从一个信息,从头,从头,从头,从一个情报网络,从头,从头,从头,从头,从头,从一个