ProjectionBands

Mel Widner's forward-projected high/low envelope: fit a separate regression to the highs and to the lows, slide every bar forward along its slope, and take the running max / min.

Quick reference

Field	Value
Family	Bands & Channels
Input type	Candle (uses high, low; open/close ignored)
Output type	ProjectionBandsOutput { upper, middle, lower }
Output range	unbounded; lower ≤ middle ≤ upper
Default parameters	period = 14
Warmup period	period (exact — first emission on bar period)
Interpretation	Trend-tilted channel that by construction contains every projected high and low in the window.

Formula

slope_h = OLS slope of (x, high) over the window      x = 0..period-1
slope_l = OLS slope of (x, low)  over the window
// bar i (0 = oldest, period-1 = newest) is (period-1-i) bars in the past
upper   = max over i of [ high_i + slope_h · (period-1-i) ]
lower   = min over i of [ low_i  + slope_l · (period-1-i) ]
middle  = (upper + lower) / 2

Widner ("Projection Bands and the Projection Oscillator", Technical Analysis of Stocks & Commodities, May 1995) projects each bar's high and low forward to the current bar using the regression slope of the highs and lows respectively, then reports the extreme projections as the band edges. A flat slope reduces the bands to the rolling highest-high / lowest-low — a Donchian channel — while a steep slope tilts the whole envelope with the trend. Source: crates/wickra-core/src/indicators/projection_bands.rs.

Parameters

Name	Type	Default	Constraint	Source
period	usize	14	>= 2	ProjectionBands::new (projection_bands.rs:78)

period < 2 returns [Error::InvalidPeriod] — a regression slope needs at least two points. Python defaults come from #[pyo3(signature = (period=14))]; the Node constructor takes the period explicitly.

Inputs / Outputs

use wickra::{Indicator, ProjectionBands, Candle, ProjectionBandsOutput};
// ProjectionBands: Input = Candle, Output = ProjectionBandsOutput
const _: fn(&mut ProjectionBands, Candle) -> Option<ProjectionBandsOutput> =
    <ProjectionBands as Indicator>::update;

• Python streaming. update(candle) returns (upper, middle, lower) or None.
• Python batch. ProjectionBands.batch(high, low) returns an (n, 3)np.ndarray with columns [upper, middle, lower]; warmup rows are NaN.
• Node streaming. update(high, low) returns a { upper, middle, lower } object or null.
• Node batch. batch(high, low) returns a flat Array<number> of length n * 3 interleaved per row [u0, m0, l0, u1, m1, l1, …].

Warmup

warmup_period() reports period and the figure is exact: both regressions need a full window before the bands are defined, so the first non-None output lands on candle period (index period − 1). Readiness is pinned by the warms_up_then_emits test (the first two updates return None, the third returns Some for period = 3).

Edge cases

• Perfect trend. When highs and lows rise by a constant amount each bar, every projected high collapses onto the current high and every projected low onto the current low, so the bands hug the latest bar's extremes — pinned by perfect_trend_pins_bands_to_current_extremes.
• Ordering. upper ≥ middle ≥ lower always holds because middle is their midpoint and upper ≥ lower by construction.
• Reset. reset() clears both high/low deques; the next update restarts the warmup countdown (test reset_clears_state).
• Non-finite inputs. Candle::new rejects non-finite OHLC up front, so the indicator never sees NaN/inf.

Examples

Rust

use wickra::{BatchExt, Candle, Indicator, ProjectionBands};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    // (high, low): (10, 8), (12, 9), (11, 10).
    let candles = vec![
        Candle::new(8.0, 10.0, 8.0, 9.0, 1.0, 0)?,
        Candle::new(9.0, 12.0, 9.0, 11.0, 1.0, 1)?,
        Candle::new(10.0, 11.0, 10.0, 11.0, 1.0, 2)?,
    ];
    let mut pb = ProjectionBands::new(3)?;
    for v in pb.batch(&candles) {
        println!("{:?}", v);
    }
    Ok(())
}

Output:

None
None
Some(ProjectionBandsOutput { upper: 12.5, middle: 11.25, lower: 10.0 })

Highs 10, 12, 11 give slope_h = 0.5; the projected highs are 11, 12.5, 11 so upper = 12.5. Lows 8, 9, 10 give slope_l = 1.0; the projected lows are all 10 so lower = 10. This matches the known_projection test.

Python

import numpy as np
import wickra as ta

pb = ta.ProjectionBands(3)
high = np.array([10.0, 12.0, 11.0])
low  = np.array([8.0, 9.0, 10.0])
print(pb.batch(high, low))

Output:

[[  nan   nan   nan]
 [  nan   nan   nan]
 [12.5  11.25 10.  ]]

Node

const ta = require('wickra');
const pb = new ta.ProjectionBands(3);
pb.update(10, 8);
pb.update(12, 9);
console.log(pb.update(11, 10)); // { upper: 12.5, middle: 11.25, lower: 10 }

Interpretation

Projection Bands answer "how far has price stretched relative to its own trend?" Because the envelope is built from the projected extremes rather than a dispersion statistic, price physically cannot close outside the bands within the fitting window — the bands act as a dynamic, slope-aware support/resistance pair:

1. Trend channel. In a steady advance the bands tilt up together; a close that repeatedly tags the upper band signals trend strength, not an immediate reversal.
2. Squeeze. When upper − lower contracts the recent range has narrowed — often a precursor to expansion, the same logic as a Bollinger squeeze but range-based.

Pair with the ProjectionOscillator to read the close's position inside the bands as a bounded 0..100 value.

Common pitfalls

• Expecting breakouts. Unlike Bollinger Bands, a close cannot pierce Projection Bands inside the window — use the band slope and width, or the oscillator, for signals rather than waiting for a pierce.
• Tiny periods. period = 2 makes the regression interpolate two points exactly; use a longer window (10–20) for a meaningful slope estimate.

References

• Mel Widner, "Projection Bands and the Projection Oscillator," Technical Analysis of Stocks & Commodities, vol. 13, May 1995.

See also

• ProjectionOscillator — the close's position inside these bands.
• Donchian — the zero-slope limit (pure rolling high/low).
• LinRegChannel — close-regression endpoint ± σ.
• StandardErrorBands — close-regression ± standard error.