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Despite the impressive success of deep neural networks in many applicationareas, neural network models have so far not been widely adopted in the contextof volatility forecasting. In this work, we aim to bridge the conceptual gapbetween established time series approaches, such as the HeterogeneousAutoregressive (HAR) model, and state-of-the-art deep neural network models.The newly introduced HARNet is based on a hierarchy of dilated convolutionallayers, which facilitates an exponential growth of the receptive field of themodel in the number of model parameters. HARNets allow for an explicitinitialization scheme such that before optimization, a HARNet yields identicalpredictions as the respective baseline HAR model. Particularly when consideringthe QLIKE error as a loss function, we find that this approach significantlystabilizes the optimization of HARNets. We evaluate the performance of HARNetswith respect to three different stock market indexes. Based on this evaluation,we formulate clear guidelines for the optimization of HARNets and show thatHARNets can substantially improve upon the forecasting accuracy of theirrespective HAR baseline models. In a qualitative analysis of the filter weightslearnt by a HARNet, we report clear patterns regarding the predictive power ofpast information. Among information from the previous week, yesterday and theday before, yesterday's volatility makes by far the most contribution totoday's realized volatility forecast. Moroever, within the previous month, theimportance of single weeks diminishes almost linearly when moving further intothe past.

HARNet: A Convolutional Neural Network for Realized Volatility Forecasting