TD REI (Range Expansion Index)

DeMark's Range Expansion Index. A short-window (default 5-bar) oscillator that conditionally weights the high/low expansions of each bar — bars where the high or low has not expanded relative to the recent baseline are zero-weighted — then normalises the signed expansion to a [-100, +100] range. Designed as a fast short-cycle momentum oscillator within DeMark's larger toolset.

Quick reference

Item	Value
Family	DeMark
Input type	Candle (uses high, low, close)
Output type	f64
Output range	[-100, +100]
Default parameters	period = 5
Warmup period	period + 7 (conditional weights need a 7-bar baseline)
Interpretation	Above +60 overbought; below −60 oversold; near 0 neutral

Formula

For each bar within the window:

condition_up = (high_t >= max(close_{t-2}, close_{t-3}))   // expansion up
condition_dn = (low_t  <= min(close_{t-2}, close_{t-3}))   // expansion down

w = 1 if (condition_up AND high_t >= low_{t-5} AND high_t >= low_{t-6})
    AND (condition_dn AND low_t <= high_{t-5} AND low_t <= high_{t-6})
    else 0

num = sum over period: w · ((high_t − high_{t-2}) + (low_t − low_{t-2}))
den = sum over period: w · (|high_t − high_{t-2}| + |low_t − low_{t-2}|)

REI = 100 · num / den         (0 if den == 0)

The conditional weighting filters out bars that don't represent a "genuine" range expansion. See crates/wickra-core/src/indicators/td_rei.rs.

Parameters

Name	Type	Default	Constraint	Description
period	usize	5	> 0	Rolling-sum window. Most DeMark literature uses 5.

TdRei::classic() constructs the 5-period default. new returns Error::PeriodZero for period == 0.

Inputs / Outputs

Indicator<Input = Candle, Output = f64>. Python: TdRei(period).batch(high, low, close) returns a 1-D np.ndarray with NaN in the warmup prefix. Node: same shape; update(candle) returns number | null.

Warmup

warmup_period() == period + 7. The 7-bar lag is the maximum look-back inside the conditional-weight check (low_{t-5}, low_{t-6} etc.).

Edge cases

• All weights zero. Indicator returns 0.0 (neutral). Common in ranging markets where neither high nor low has expanded.
• Pure expansion up. All weighted differences positive → REI approaches +100.
• Reset. Clears the rolling buffers.

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let candles: Vec<Candle> = (0..30).map(|i| {
        let b = 100.0 + f64::from(i);
        Candle::new(b, b + 1.0, b - 1.0, b, 1.0, i as i64).unwrap()
    }).collect();
    let mut r = TdRei::classic();
    println!("row 20 = {:?}", r.batch(&candles)[20]);
    Ok(())
}

Python

import numpy as np
import wickra as ta

base = 100 + np.arange(30, dtype=float)
r = ta.TdRei(5)
out = r.batch(base + 1, base - 1, base)
print('warmup:', r.warmup_period())  # 12
print('row 20:', out[20])

Node

const wickra = require('wickra');
const r = new wickra.TdRei(5);
const base = Array.from({ length: 30 }, (_, i) => 100 + i);
console.log('row 20:',
  r.batch(base.map(b => b + 1), base.map(b => b - 1), base)[20]);

Streaming

use wickra::{Candle, Indicator, TdRei};

let mut r = TdRei::classic();
let candle_stream: Vec<wickra::Candle> = Vec::new(); // your live OHLCV candle feed
for bar in candle_stream {
    if let Some(v) = r.update(bar) {
        if v > 60.0 { /* overbought */ }
        if v < -60.0 { /* oversold */ }
    }
}

Interpretation

REI is the short-window momentum oscillator in the DeMark toolbox:

• REI > +60. Recent range expansion has been dominated by new highs — overbought.
• REI < −60. Range expansion dominated by new lows — oversold.
• Persistent zero readings. No genuine range expansion in either direction; the market is consolidating.
• As Sequential precondition. Some DeMark traders use REI > +45 / < −45 as a momentum gate for TD Sequential signals — REI confirms the momentum context.

Common pitfalls

• Comparing REI to RSI thresholds. Different scales (-100..+100 vs 0..100) and different neutral points (0 vs 50).
• Reading every zero-cross. REI sits at zero for long periods in ranges; only the move off zero is meaningful.
• Conditional-weight surprise. Two seemingly-similar price patterns can produce very different REI readings because the weight gate kicks in differently. The implementation matches DeMark's published rules exactly; if you're getting unexpected output, compare against the rule, not against your intuition.

References

• Tom DeMark, The New Science of Technical Analysis (1994), ch. 4: Range Expansion Index.

See also

• TdDeMarker — wider-window DeMark momentum oscillator.
• TdPressure — volume-aware DeMark momentum sibling.
• TdSequential — paired with REI for confirmation in some setups.
• Rsi — close-based momentum analogue.
• Indicators-Overview — full taxonomy.