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A pairs trading strategy based on linear state space models and the Kalman filter

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  • Carlos Eduardo de Moura
  • Adrian Pizzinga
  • Jorge Zubelli

Abstract

Among many strategies for financial trading, pairs trading has played an important role in practical and academic frameworks. Loosely speaking, it involves a statistical arbitrage tool for identifying and exploiting the inefficiencies of two long-term, related financial assets. When a significant deviation from this equilibrium is observed, a profit might result. In this paper, we propose a pairs trading strategy entirely based on linear state space models designed for modelling the spread formed with a pair of assets. Once an adequate state space model for the spread is estimated, we use the Kalman filter to calculate conditional probabilities that the spread will return to its long-term mean. The strategy is activated upon large values of these conditional probabilities: the spread is bought or sold accordingly. Two applications with real data from the US and Brazilian markets are offered, and even though they probably rely on limited evidence, they already indicate that a very basic portfolio consisting of a sole spread outperforms some of the main market benchmarks.

Suggested Citation

  • Carlos Eduardo de Moura & Adrian Pizzinga & Jorge Zubelli, 2016. "A pairs trading strategy based on linear state space models and the Kalman filter," Quantitative Finance, Taylor & Francis Journals, vol. 16(10), pages 1559-1573, October.
    • Handle: RePEc:taf:quantf:v:16:y:2016:i:10:p:1559-1573
    DOI: 10.1080/14697688.2016.1164886
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    References listed on IDEAS

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    1. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, Decembrie.
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    Cited by:

    1. Baoqiang Zhan & Shu Zhang & Helen S. Du & Xiaoguang Yang, 2022. "Exploring Statistical Arbitrage Opportunities Using Machine Learning Strategy," Computational Economics, Springer;Society for Computational Economics, vol. 60(3), pages 861-882, October.
    2. Choi, Gahyun & Park, Kwangyeol & Yi, Eojin & Ahn, Kwangwon, 2023. "Price fairness: Clean energy stocks and the overall market," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    3. Matthew Clegg & Christopher Krauss, 2018. "Pairs trading with partial cointegration," Quantitative Finance, Taylor & Francis Journals, vol. 18(1), pages 121-138, January.
    4. Adrian Pizzinga & Marcelo Fernandes, 2021. "Extensions to the invariance property of maximum likelihood estimation for affine‐transformed state‐space models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(3), pages 355-371, May.
    5. Trent Spears & Stefan Zohren & Stephen Roberts, 2023. "On statistical arbitrage under a conditional factor model of equity returns," Papers 2309.02205, arXiv.org.
    6. Clegg, Matthew & Krauss, Christopher, 2016. "Pairs trading with partial cointegration," FAU Discussion Papers in Economics 05/2016, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    7. Chu, Gang & Zhang, Wei & Sun, Guofeng & Zhang, Xiaotao, 2019. "A new online portfolio selection algorithm based on Kalman Filter and anti-correlation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    8. Guang Zhang, 2020. "Pairs Trading with Nonlinear and Non-Gaussian State Space Models," Papers 2005.09794, arXiv.org.
    9. Kasper Johansson & Thomas Schmelzer & Stephen Boyd, 2024. "Finding Moving-Band Statistical Arbitrages via Convex-Concave Optimization," Papers 2402.08108, arXiv.org.
    10. Sana Ben Abdallah & Dhafer Saidane & Mihaly Petreczky, 2023. "Application of Robust Control for CSR Formalization and Stakeholders Interest," Computational Economics, Springer;Society for Computational Economics, vol. 62(3), pages 891-934, October.

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