# HARNet: A Convolutional Neural Network for Realized Volatility Forecasting

arXiv: https://arxiv.org/abs/2205.07719 · HTML: https://mlsanity.com/paper/2205.07719/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 31 references that are in the map.
- First posted on arXiv 16 May 2022.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [Convolutional Sequence to Sequence Learning](https://mlsanity.com/paper/1705.03122/) (2017)
- [Conditional Time Series Forecasting with Convolutional Neural Networks](https://mlsanity.com/paper/1703.04691/) (2017)
- [Neural Machine Translation in Linear Time](https://mlsanity.com/paper/1610.10099/) (2016)
- [A Convolutional Encoder Model for Neural Machine Translation](https://mlsanity.com/paper/1611.02344/) (2016)

## Built on by (most cited first, 3 of 3)

- [DeepVol: Volatility Forecasting from High-Frequency Data with Dilated Causal Convolutions](https://mlsanity.com/paper/2210.04797/) (2022)
- [Generalized Autoregressive Score Trees and Forests](https://mlsanity.com/paper/2305.18991/) (2023)
- [Same Error, Different Function: The Optimizer as an Implicit Prior in Financial Time Series](https://mlsanity.com/paper/2603.02620/) (2026)

## Abstract (arXiv)

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.