# Neural Augmented Kalman Filtering with Bollinger Bands for Pairs Trading

arXiv: https://arxiv.org/abs/2210.15448 · HTML: https://mlsanity.com/paper/2210.15448/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 76 references that are in the map.
- First posted on arXiv 19 Oct 2022.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction](https://mlsanity.com/paper/1704.02971/) (2017)
- [Model-Based Deep Learning](https://mlsanity.com/paper/2012.08405/) (2020)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Deep Learning for Time Series Forecasting: Tutorial and Literature Survey](https://mlsanity.com/paper/2004.10240/) (2020)
- [Model-Based Deep Learning: On the Intersection of Deep Learning and Optimization](https://mlsanity.com/paper/2205.02640/) (2022)
- [Market Making via Reinforcement Learning](https://mlsanity.com/paper/1804.04216/) (2018)
- [A Hybrid DSP/Deep Learning Approach to Real-Time Full-Band Speech Enhancement](https://mlsanity.com/paper/1709.08243/) (2017)
- [Reinforcement Learning for Quantitative Trading](https://mlsanity.com/paper/2109.13851/) (2021)
- [Weighted Speech Distortion Losses for Neural-network-based Real-time Speech Enhancement](https://mlsanity.com/paper/2001.10601/) (2020)
- [Unsupervised Learned Kalman Filtering](https://mlsanity.com/paper/2110.09005/) (2021)
- [Discriminative and Generative Learning for Linear Estimation of Random Signals [Lecture Notes]](https://mlsanity.com/paper/2206.04432/) (2022)
- [Improving Stock Market Prediction via Heterogeneous Information Fusion](https://mlsanity.com/paper/1801.00588/) (2018)
- [Deep Task-Based Analog-to-Digital Conversion](https://mlsanity.com/paper/2201.12634/) (2022)

## Built on by (most cited first, 2 of 2)

- [QuantFactor REINFORCE: Mining Steady Formulaic Alpha Factors with Variance-bounded REINFORCE](https://mlsanity.com/paper/2409.05144/) (2024)
- [AI-Aided Kalman Filters](https://mlsanity.com/paper/2410.12289/) (2024)

## Abstract (arXiv)

Pairs trading is a family of trading techniques that determine their policies based on monitoring the relationships between pairs of assets. A common pairs trading approach relies on describing the pair-wise relationship as a linear Space State (SS) model with Gaussian noise. This representation facilitates extracting financial indicators with low complexity and latency using a Kalman Filter (KF), that are then processed using classic policies such as Bollinger Bands (BB). However, such SS models are inherently approximated and mismatched, often degrading the revenue. In this work, we propose KalmenNet-aided Bollinger bands Pairs Trading (KBPT), a deep learning aided policy that augments the operation of KF-aided BB trading. KBPT is designed by formulating an extended SS model for pairs trading that approximates their relationship as holding partial co-integration. This SS model is utilized by a trading policy that augments KF-BB trading with a dedicated neural network based on the KalmanNet architecture. The resulting KBPT is trained in a two-stage manner which first tunes the tracking algorithm in an unsupervised manner independently of the trading task, followed by its adaptation to track the financial indicators to maximize revenue while approximating BB with a differentiable mapping. KBPT thus leverages data to overcome the approximated nature of the SS model, converting the KF-BB policy into a trainable model. We empirically demonstrate that our proposed KBPT systematically yields improved revenue compared with model-based and data-driven benchmarks over various different assets.