Neural Augmented Kalman Filtering With Bollinger Bands for Pairs Trading

Amit Milstein, Guy Revach, Haoran Deng, Hai Morgenstern, Nir Shlezinger

Research output: Contribution to journalArticlepeer-review


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 pairwise 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), which 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 KalmanNet-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 assets.

Original languageEnglish
Pages (from-to)1974-1988
Number of pages15
JournalIEEE Transactions on Signal Processing
StatePublished - 1 Jan 2024


  • Kalman filter
  • KalmanNet
  • Pairs trading
  • model based deep learning
  • quantitative strategies

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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