Adaptive Bollinger band impulse, trend, and momentum filters

One envelope, three complementary filters

Bollinger bands are a volatility envelope around a moving average that scales other indicators so readings adapt to how wide or tight the market is. The archive workflow starts from that single envelope and converts the same ordered price series into percent-b, BandWidth, and a family of band-relative filters.

Those filters are complementary rather than redundant. BB Impulse is a one-period snapshot of how hard price is pushing toward a band. BB Momentum stretches the same idea across a multi-period window. BB Trend asks whether envelopes of different lookbacks are aligned in a trending or a nontrending way.

Percent-b and BandWidth

Percent-b is a normalized reading of where price sits between the lower and upper bands. It places price at 1 on the upper band, 0 on the lower band, and 0.5 on the middle average.

BandWidth measures how wide the envelope is by using the middle average as the reference, so the same chart shows how expanded or compressed the envelope is. Together they give later filters a scale that already knows whether the market is tight or wide.

BB Impulse as a one-period snapshot

BB Impulse is defined as this period's percent-b minus last period's percent-b. Because the subtraction is applied to a band-relative reading, the filter captures both price change and changing band width.

Because BB Impulse is band-relative, a modest move can print a large reading when bands are tight and a smaller reading when bands are wide. The reading is an adaptive snapshot of whether price is pushing harder toward one band or the other after the envelope itself has been allowed to expand or contract.

BB Momentum as a multi-period reading

BB Momentum expresses price change over a multi-period window, such as 10 periods, as a function of the bands rather than as an unscaled rate of change. The same price move therefore looks large in a tight range and small in a volatile trend.

BB Trend from aligned envelopes

BB Trend compares alignments of different-period envelopes, such as 20-period and 50-period bands, to distinguish trending from nontrending conditions.

In an intermediate uptrend the upper 20-period and 50-period bands tend to run nearly together. A strong downtrend shows similar alignment on the lower bands.

BB Trend is signed from +1 to -1, so strong readings above zero mark a positive trend and strong readings below zero mark a negative trend.

Three pushes to a high

A three-pushes-to-a-high sequence is a topping pattern in which later advances lose impulse and trend strength even if price still makes a high, often with the third advance acting as a retest.

In that sequence, BB Impulse prints steadily lower groups of positive readings, BB Trend fades near the second push, and BB Momentum makes lower highs, with the third-push reading clearly below the first or second. The three filters are describing the same series from different windows: a weakening push, a fading trend alignment, and a momentum high that fails to confirm.

A smooth-valued stance

A later modeling choice replaced binary and three-state long-flat-short logic with a smooth-valued stance so partial long or short exposure can be expressed. Smooth-valued logic is a graded long-to-short stance that allows partial exposure instead of forcing a binary long-or-short decision.