DerivativeOscillator

Derivative Oscillator — Constance Brown's double-EMA-smoothed RSI minus an SMA signal, a zero-centered momentum histogram that strips RSI noise.

Quick reference

Field	Value
Family	Momentum Oscillators
Input type	f64 (single price)
Output type	f64 (histogram, centered on 0)
Output range	unbounded; oscillates around 0
Default parameters	rsi_period, smooth1, smooth2, signal_period (Brown: 14, 5, 3, 9)
Warmup period (warmup_period())	rsi_period + smooth1 + smooth2 + signal_period − 2
Interpretation	Sign and slope of accelerating momentum.

Formula

rsi    = RSI(price, rsi_period)
s1     = EMA(rsi, smooth1)
s2     = EMA(s1,  smooth2)             // double-smoothed RSI
signal = SMA(s2, signal_period)
DerivativeOscillator = s2 - signal

The double EMA pass removes the RSI's jitter; subtracting the SMA signal removes the residual level, leaving a histogram centered on zero. Positive, rising bars mark accelerating bullish momentum; negative, falling bars bearish. Because a constant RSI (a steady trend) double-smooths to itself and equals its own signal, the oscillator reads exactly 0 — the histogram measures the change in momentum, not its level.

Source: crates/wickra-core/src/indicators/derivative_oscillator.rs.

Parameters

Name	Type	Default	Valid range	Source	Description
rsi_period	usize	14	>= 1	derivative_oscillator.rs:62	Wilder RSI period.
smooth1	usize	5	>= 1	derivative_oscillator.rs:62	First EMA smoothing of the RSI.
smooth2	usize	3	>= 1	derivative_oscillator.rs:62	Second EMA smoothing.
signal_period	usize	9	>= 1	derivative_oscillator.rs:62	SMA signal subtracted to center it.

Any zero period errors with Error::PeriodZero. (Python wickra.DerivativeOscillator(rsi_period, smooth1, smooth2, signal_period); Node new ta.DerivativeOscillator(...).)

Inputs / Outputs

From crates/wickra-core/src/indicators/derivative_oscillator.rs:

use wickra::{DerivativeOscillator, Indicator};
// DerivativeOscillator: Input = f64, Output = f64
const _: fn(&mut DerivativeOscillator, f64) -> Option<f64> =
    <DerivativeOscillator as Indicator>::update;

Python returns float | None (streaming) / numpy.ndarray (batch, NaN for warmup). Node returns number | null / Array<number> with NaN.

Warmup

warmup_period() returns rsi_period + smooth1 + smooth2 + signal_period − 2: the RSI seeds at rsi_period + 1, then each EMA adds len − 1 and the SMA adds signal_period − 1. For the (14, 5, 3, 9) defaults that is 29. Pinned by accessors_and_metadata (warmup() == 29) and first_emission_matches_warmup_period (first Some exactly at index warmup_period() − 1).

Edge cases

• Constant momentum → 0. A steady trend pins the RSI, which double-smooths to itself and equals its signal, so the histogram is 0; shown in the example below and implied by matches_manual_chain.
• Equivalence to the manual chain. matches_manual_chain runs RSI → EMA → EMA, minus SMA, alongside and asserts equality bar-for-bar.
• Zero periods. rejects_zero_periods pins the Error::PeriodZero path for each of the four arguments.
• Reset. reset_clears_state. Streaming/batch: batch_equals_streaming.

Examples

Rust

use wickra::{BatchExt, DerivativeOscillator, Indicator};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut d = DerivativeOscillator::new(3, 2, 2, 3)?;
    let prices: Vec<f64> = (1..=15).map(f64::from).collect();
    let out: Vec<Option<f64>> = d.batch(&prices);
    println!("warmup_period = {}", d.warmup_period());
    println!("{:?}", out);
    Ok(())
}

Output:

warmup_period = 8
[None, None, None, None, None, None, None, Some(0.0), Some(0.0), Some(0.0), Some(0.0), Some(0.0), Some(0.0), Some(0.0), Some(0.0)]

On the steady uptrend the RSI pins at 100; double-smoothed it stays 100 and its SMA signal is also 100, so the histogram is exactly 0 — momentum is strong but not accelerating.

Python

import numpy as np
import wickra as ta

d = ta.DerivativeOscillator(3, 2, 2, 3)
out = d.batch(np.arange(1.0, 16.0))
print("warmup_period =", d.warmup_period())
print(out)

Output:

warmup_period = 8
[nan nan nan nan nan nan nan  0.  0.  0.  0.  0.  0.  0.  0.]

Node

const ta = require('wickra');
const d = new ta.DerivativeOscillator(3, 2, 2, 3);
const prices = Array.from({ length: 15 }, (_, i) => i + 1);
console.log(d.batch(prices));
console.log('warmupPeriod:', d.warmupPeriod());

Output:

[
  NaN, NaN, NaN, NaN, NaN,
  NaN, NaN,   0,   0,   0,
    0,   0,   0,   0,   0
]
warmupPeriod: 8

Streaming

use wickra::{DerivativeOscillator, Indicator};

let mut d = DerivativeOscillator::new(14, 5, 3, 9)?;
let mut last = None;
for i in 0..120 {
    last = d.update(100.0 + (f64::from(i) * 0.2).sin() * 5.0);
}
println!("{last:?}"); // oscillates around 0 with the momentum cycle
# Ok::<(), Box<dyn std::error::Error>>(())

Interpretation

The Derivative Oscillator answers "is momentum accelerating?" rather than "is the market overbought?". Because it is the change of a smoothed RSI around its own average, it leads the RSI's own turns slightly and filters the chop that makes a raw RSI hard to read on intraday data.

Typical uses:

1. Zero-line crosses. Histogram crossing above zero = momentum turning up; below = turning down.
2. Histogram slope. Rising bars (even below zero) signal momentum building; shrinking bars warn of a stall before the zero cross.
3. Divergence. Price highs with lower histogram peaks flag fading thrust.

Common pitfalls

• Reading zero as "no trend". A flat-zero reading means constant momentum (often a strong, steady trend), not the absence of one.
• Parameter sprawl. Four periods interact; start from Brown's (14, 5, 3, 9) and change one at a time.

References

Constance Brown, Technical Analysis for the Trading Professional, 1999 — the Derivative Oscillator.

See also

• Indicator-Rsi — the underlying oscillator.
• Indicator-Tsi — another double-smoothed momentum measure.
• Indicator-MacdIndicator — histogram-style momentum on price EMAs.
• Indicators-Overview — the full taxonomy.