TD REI (Range Expansion Index)

DeMark's Range Expansion Index. A short-window (default 5-bar) oscillator that sums each bar's signed high/low change versus two bars earlier — counted in the numerator only when the bar's range overlaps the bars 5–6 back, or the bar two back overlaps the closes 7–8 back — and divides by the sum of the absolute changes of every bar, giving 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	8 + period (the conditions look back 8 bars; classic 13)
Interpretation	Above +60 overbought; below −60 oversold; near 0 neutral

Formula

For each bar t (history through t − 8 required):

overlap      = (high_t     >= low_{t-5}   OR high_t     >= low_{t-6})
           AND (low_t      <= high_{t-5}  OR low_t      <= high_{t-6})
overlap_back = (high_{t-2} >= close_{t-7} OR high_{t-2} >= close_{t-8})
           AND (low_{t-2}  <= close_{t-7} OR low_{t-2}  <= close_{t-8})

num_t = (high_t − high_{t-2}) + (low_t − low_{t-2})   if overlap OR overlap_back
      = 0                                             otherwise
den_t = |high_t − high_{t-2}| + |low_t − low_{t-2}|   (every bar)

REI = 100 · Σ_period num / Σ_period den, clamped to [-100, +100]
      (0 if Σ den == 0)

The gate only zeroes the numerator: a bar whose range does not overlap the bars 5–6 back (and whose bar-two-back does not overlap the closes 7–8 back — DeMark's alternative condition) still adds its absolute change to the denominator, pulling REI towards zero. Since |num_t| ≤ den_t bar by bar, the ratio is bounded; the clamp only absorbs last-bit rounding. 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 an array.array('d') with NaN in the warmup prefix (close is required — the alternative condition reads the closes 7–8 bars back). Node and WASM: batch(high, low, close) returns number[] (NaN warmup); update(high, low, close) returns number | null.

Warmup

warmup_period() == 8 + period (13 for the classic 5-bar window). The first 8 bars only fill the look-back (the alternative condition reaches close_{t-8}); then period per-bar numerator / denominator terms fill the window, so the first value lands at index 8 + period − 1 (index 12 for period = 5).

Edge cases

• Zero denominator. When highs and lows do not change over the window the indicator returns 0.0 (neutral) (flat_market_yields_neutral_zero).
• Gate closed. Bars failing both overlap conditions add 0 to the numerator but their full change to the denominator, so a steep, tight-ranged trend can read near 0.
• Pure expansion up / down. A slow steady trend (slope 0.1, spread 2) passes the gate every bar → REI saturates at +100 (pure_uptrend_pegs_indicator_at_100) or −100 (pure_downtrend_pegs_indicator_at_minus_100).
• Bounded. Output stays in [-100, +100] (stays_in_minus_100_to_100).
• Zero period. TdRei::new(0) errors (rejects_zero_period).
• Reset. Clears the rolling buffers (reset_clears_state).

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) * 0.1;
        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]); // row 20 = Some(100.0)
    Ok(())
}

Python

import numpy as np
import wickra as ta

base = 100 + np.arange(30, dtype=float) * 0.1
r = ta.TDREI(5)
out = r.batch(base + 1, base - 1, base)
print('warmup:', r.warmup_period())  # 13
print('row 20:', out[20])            # 100.0

Node

const wickra = require('wickra');
const r = new wickra.TDREI(5);
const base = Array.from({ length: 30 }, (_, i) => 100 + i * 0.1);
console.log('row 20:',
  r.batch(base.map(b => b + 1), base.map(b => b - 1), base)[20]); // row 20: 100

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. Either highs and lows are not changing, or bars keep failing the overlap gate (their changes count only in the denominator); the market has no qualified range expansion in either direction.
• 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-gate surprise. Two seemingly-similar price patterns can produce very different REI readings because the overlap gate (or its close-based alternative) 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.
• Jason Perl, DeMark Indicators (Bloomberg Press, 2008) — TD REI conditions, including the alternative close-based condition.

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.