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Bollinger Bands and Statistical Methods for Pairs Trading

Article arXiv papers · Author: Mark Leeds
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Summary

The study examines the statistical basis of Bollinger Bands by connecting them to a rolling regression time-series model. It applies the framework to pairs trading and derives a relationship between trade duration and returns for strategies based on the bands.

The authors also interpret the moving average in Bollinger Bands as an approximation to a random walk plus noise model, then develop a variant called Fixed Forecast Maximum Duration Bands. Simulations using SAP and Nikkei index data compare this variant with conventional Bollinger Bands. The document describes the methods and comparison but provides no numerical results, so it does not establish which approach performs better or whether the findings generalize beyond the selected assets and simulation design.

Key ideas

  • A rolling regression model provides a statistical interpretation of Bollinger Bands.
  • Bollinger Bands can be used to construct pairs trading strategies.
  • The paper derives a relationship between returns and trade duration in band-based pairs trading.
  • A random walk plus noise approximation motivates a fixed forecast maximum duration variant.
  • Simulations on SAP and Nikkei data compare the variant with standard Bollinger Bands.

Tags

Pairs tradingMean reversionTechnical indicatorsStatisticsBacktesting
Full text
# Bollinger Bands Thirty Years Later


# Bollinger Bands Thirty Years Later









The goal of this study is to explain and examine the statistical underpinnings of the Bollinger Band methodology. We start off by elucidating the rolling regression time series model and deriving its explicit relationship to Bollinger Bands. Next we illustrate the use of Bollinger Bands in pairs trading and prove the existence of a specific return duration relationship in Bollinger Band pairs trading.Then by viewing the Bollinger Band moving average as an approximation to the random walk plus noise (RWPN) time series model, we develop a pairs trading variant that we call "Fixed Forecast Maximum Duration' Bands" (FFMDPT). Lastly, we conduct pairs trading simulations using SAP and Nikkei index data in order to compare the performance of the variant with Bollinger Bands.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.