Combination filters with Bollinger Bands and the relative strength index

Two stages, not one line

An envelope is a three-line price channel built from a central moving average plus upper and lower boundaries that mark temporary extremes around the trend. A combination-filter does not treat those extremes as complete signals. It waits for a second, independent check from the relative strength index, an oscillator that measures the speed and magnitude of recent price changes.

Fixed width versus adaptive width

Fixed-percentage envelopes place the upper and lower lines a constant fraction of a moving average away from that average. Channel width then stays the same when volatility changes.

Bollinger Bands replace that fixed fraction with a multiple of the standard deviation of price. Bandwidth is then tied to the observed price series rather than to an arbitrary percentage. That construction is standard-deviation-bandwidth. A common setting uses two standard deviations because, in a normal distribution, most values fall within two standard deviations of the mean. From that fact the archive infers that most of a stock's price action should stay between the bands.

On one historical sample, the two-standard-deviation bands contained more of the price bars than a fixed-percentage envelope around a simple moving average, including during sharp moves.

Squeeze-and-expansion and input choice

The bands widen when volatility is high and contract when volatility is low. That squeeze-and-expansion is the visible difference from a fixed envelope. On one sample the bands were much wider in a volatile week than during a quieter stretch.

The moving-average length is chosen to match the trend horizon being followed. The bands may be computed from closes or from alternative inputs such as typical-price or weighted-close. Typical-price is formed from the high, low, and close of each bar. Weighted-close weights the close twice as heavily as the high and the low.

Confirming the extreme

The archive combines Bollinger Bands with the relative strength index so that band extremes are used only when the oscillator confirms. That rule set is the combination-filter. It was written in explicit long-and-short form and in a long-only-variant that keeps the same logic but restricts entries and exits to the long side.

Those variants were placed next to a buy-and-hold-baseline, an explicit comparison path that stays fully invested over the same sample window. The tested rules included no stop-loss provisions. The archive treats that omission as a reason a practical system would have exited a large losing short well before the drawdown ran its course.

How to use a comparison window

A combination that fails on one stock and window is not thereby dismissed. The archive's conclusion is that usefulness depends on market selection, historical testing, money management, and the trader's style, because no method works for all stocks in all conditions.

Editorial reading: keep the two-sided rules, the long-only-variant, and the buy-and-hold-baseline in one comparison so the stack can be inspected. The comparison is a design check, not a contest to name a winner.