Bollinger Bands

Bollinger Bands (20-period, 2-sigma default). Returns upper / mid / lower band arrays. Edge-first on an upstream close series. Wired to more than one Price Factor, it fans out to per-ticker by_symbol results.

What (One-liner)

Volatility envelope around a moving average (20-day SMA ± 2σ) — feeds breakout and mean-reversion signals.

Inputs

• period (number, optional) — lookback, default 20.
• std_dev (number, optional) — band width in sigmas, default 2.

Outputs

• upper — mid + std_dev × sigma.
• mid — middle band (moving average).
• lower — mid - std_dev × sigma.
• by_symbol — per-ticker map when fed by multiple Price Factors.

How to use

1. Connect an upstream price_factor.
2. Optionally override period and std_dev.
3. Read upper / mid / lower for envelope-relative signals.

Core formulas

mid = close.rolling(period).mean()
std = close.rolling(period).std(ddof=0)
upper = mid + std_dev × std
lower = mid - std_dev × std

Assumptions & applicability

Assumptions: Bollinger 20 / 2σ defaults + ddof=0 (population std) + pandas-ta equivalent.

Applicability: mean-reversion signals, breakout identification, volatility envelope; equities, FX, crypto, commodities at daily / weekly frequency.

Out of scope: n < period, trending markets (bands hug price).

Known limitations

1. Assumes roughly normal dispersion; fat tails break band coverage.
2. Band touches are not signals on their own.
3. 20 / 2σ defaults are convention; ddof choice affects band width; pandas-ta dispatch dependency.

References

Bollinger (2001), Bollinger on Bollinger Bands; Murphy (1999), textbook explanation.

Golden Test

tests/golden/fixtures/tier1/compute_bollinger/ — tolerance 1e-10 absolute, pandas-ta + manual SMA + rolling std cross-check, last verified 2026-05-25, status passing.

Changelog

• 1.0.0 (2026-05-25) — Activated as canonical Layer-1 transform; merged governance fields from the superseded Layer-0 compute_bollinger card.