Constructing three-state filters from Bollinger band envelopes

A shared reading of the envelope

Bollinger Bands are a pair of envelopes placed a chosen multiple of standard deviation above and below a moving-average midline of an ordered price series. The moving average is the lookback smoother that supplies that midline, and the upper and lower envelopes are offset from it.

A reusable numeric state-function can classify each bar as contraction, expansion, or transition by comparing the current upper and lower volatility bands with the immediately prior band values. Indicators, paints, and later rules can then share the same envelope logic.

How the three states are assigned

Contraction is the discrete state in which the upper envelope is lower than its prior value and the lower envelope is higher than its prior value. It is the joint event that the upper band has declined and the lower band has risen relative to the previous bar.

Expansion is the discrete state in which the upper envelope is higher than its prior value and the lower envelope is lower than its prior value. It is the joint event that the upper band has risen and the lower band has declined relative to the previous bar.

Transition is the residual state assigned when neither the contraction test nor the expansion test is true.

Default lookback and band offset

The primary default construction uses a 28-period lookback and a two-standard-deviation offset on the chosen price series.

Plots that follow the shared state

Overlay studies can plot the band pair only while the state equals contraction or only while it equals expansion, so the envelope is drawn only in those phases.

Confirming bars and a sample expansion rule

A phase-counter is a running tally of consecutive bars that remain in contraction or expansion. Consecutive-occurrence counters on those two states let a later rule require more than one confirming bar before a phase is treated as established. One sample expansion trigger waits until the expansion count exceeds 1.

Once that expansion trigger is set, a sample construction arms a stop above the highest high of the prior 10 bars and a stop below the lowest low of the prior 10 bars. The supplied logic does not reset the trigger.

The same rule on a moving-average envelope

The same three-state rule can be rebuilt from a moving average plus a multiple of standard deviation. One reconstruction uses a 21-period average, and another uses an exponential average with a 28-period default.