SMI

William Blau's Stochastic Momentum Index — a doubly-EMA-smoothed bounded oscillator measuring the close's displacement from the centre of the recent high-low range.

Quick reference

Field	Value
Family	Momentum Oscillators
Input type	Candle (uses high, low, close)
Output type	f64
Output range	[−100, 100] in practice (by construction, not clamped)
Default parameters	period = 5, d_period = 3, d2_period = 3
Warmup period	period + d_period + d2_period − 2 (9 for defaults)
Interpretation	Positive in close-near-high markets, negative in close-near-low markets.

Formula

Over the lookback period, let HH = max(high), LL = min(low), C = (HH + LL) / 2, R = HH − LL. The raw displacement is d_t = close_t − C_t. Both d and R are smoothed twice with EMAs:

D_smoothed  = EMA(EMA(d, d_period), d2_period)
HL_smoothed = EMA(EMA(R, d_period), d2_period)
SMI         = 100 · D_smoothed / (HL_smoothed / 2)

Where a plain stochastic divides by the raw range, SMI divides the doubly-smoothed displacement by the doubly-smoothed half-range — far less jumpy than %K. Wickra publishes the SMI value only; the optional signal EMA(SMI, k) is left to the consumer via Chain or a manual Ema.

Parameters

Name	Type	Default	Constraint	Source
period	usize	5	>= 1	Smi::new (smi.rs:60)
d_period	usize	3	>= 1	smi.rs:60
d2_period	usize	3	>= 1	smi.rs:60

Any zero period returns [Error::PeriodZero]. Smi::classic() returns (5, 3, 3). Python defaults come from #[pyo3(signature = (period=5, d_period=3, d2_period=3))]; the Node constructor takes all three explicitly. The public class is SMI in both bindings.

Inputs / Outputs

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

Uses high, low, close.

• Python. update(candle) returns float | None; batch(high, low, close) returns a 1-D float64 np.ndarray with NaN warmup.
• Node. update(high, low, close) returns number | null; batch(high, low, close) returns an Array<number> with NaN warmup.

Warmup

warmup_period() returns period + d_period + d2_period − 2. The high-low window needs period candles; both EMA stacks (fed in parallel) then need d_period + d2_period − 2 more values. For the defaults that is 5 + 3 + 3 − 2 = 9. Pinned by warmup_emits_first_value_at_warmup_period.

Edge cases

• Close at the high. A rising series closing at its high drives SMI strongly positive (> 50) (test close_at_high_pushes_toward_plus_100).
• Close at the low. The mirror drives SMI strongly negative (< −50).
• Flat close at range centre. Displacement is 0 every bar ⇒ SMI = 0 (test flat_close_yields_zero_displacement).
• Zero range. A window where the smoothed range collapses to 0 makes the formula undefined; the indicator holds (test zero_range_holds_previous_value).
• Reset. reset() clears the high/low windows and all four EMAs.

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut smi = Smi::classic(); // (5, 3, 3)
    let mut last = None;
    for i in 0..40 {
        let p = 100.0 + f64::from(i);
        last = smi.update(Candle::new(p, p + 1.0, p - 1.0, p, 1.0, i64::from(i))?);
    }
    println!("{last:?}");
    Ok(())
}

Python

import wickra as ta
smi = ta.SMI(5, 3, 3)
out = smi.batch(high, low, close)  # 1-D series in ~[-100, 100], NaN warmup

Node

const ta = require('wickra');
const smi = new ta.SMI(5, 3, 3);
const v = smi.update(101, 99, 100); // high, low, close

Interpretation

SMI is a smoother, ±100 reinterpretation of the classic stochastic:

1. Overbought / oversold. Readings near +100 mean the close is parked near the top of the recent range (overbought); near −100 the bottom. Common thresholds are ±40.
2. Zero-line and signal crosses. A cross of zero marks the close moving from the lower to the upper half of the range; pairing SMI with its own EMA signal line gives Blau's crossover entries with far less whipsaw than raw %K/%D.

Common pitfalls

• Expecting hard clamping. SMI is bounded [−100, 100] only by construction on well-behaved data; it is not explicitly clamped, so pathological inputs can stray slightly.
• Confusing it with a plain stochastic. The double EMA smoothing makes SMI lag a raw stochastic — that lag is the point.

References

• William Blau, "The Stochastic Momentum Index", Technical Analysis of Stocks & Commodities, 1993.

See also

• Stochastic — the raw %K/%D SMI smooths.
• StochRsi — stochastic applied to RSI.
• Tsi — Blau's True Strength Index, the same double-EMA idea on momentum.