Bollinger Bands Thirty Years Later

TL;DR

This paper explores the statistical foundations of Bollinger Bands, introduces a new trading variant called FFMDPT, and compares its performance with traditional Bollinger Bands through empirical simulations.

Contribution

It provides a detailed statistical analysis of Bollinger Bands, derives a new pairs trading method called FFMDPT, and empirically evaluates its effectiveness.

Findings

Derives explicit relationship between Bollinger Bands and rolling regression models.

Proves a return duration relationship in Bollinger Band pairs trading.

Shows FFMDPT can outperform traditional Bollinger Bands in empirical tests.

Abstract

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.