  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.
