wickra/docs/wiki/indicators/moving-averages/Indicator-Smma.md

SMMA

Smoothed Moving Average — Wilder's running moving average (RMA): an SMA-seeded exponential average with a slow 1 / period smoothing factor.

Quick reference

Field	Value
Family	Moving Averages
Input type	f64 (single close)
Output type	f64
Output range	unbounded; tracks the input price scale
Default parameters	period is required (no default in either binding)
Warmup period	period
Interpretation	Heavily smoothed price level; the average underlying Wilder's RSI and ATR.

Formula

SMMA_period = SMA(price_1 … price_period)                       (seed)
SMMA_t      = (SMMA_{t-1} * (period - 1) + price_t) / period     (t > period)

This is algebraically an exponential moving average with smoothing factor alpha = 1 / period — substantially slower than the Ema factor of 2 / (period + 1) at the same period. The recurrence is O(1): each update touches only the previous value.

Parameters

Name	Type	Default	Valid range	Description
period	usize	none	>= 1	Smoothing length. period = 0 errors with Error::PeriodZero. period = 1 is a pass-through.

There is no Python #[pyo3(signature = …)] default for SMMA, so wickra.SMMA(period) requires the period explicitly.

Inputs / Outputs

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

impl Indicator for Smma {
    type Input = f64;
    type Output = f64;
    // update(&mut self, input: f64) -> Option<f64>
}

A single f64 close in, an Option<f64> out. Python maps this to float | None (streaming) or a numpy.ndarray with NaN warmup rows (batch); Node maps it to number | null / Array<number> with NaN warmup.

Warmup

Smma::new(period).warmup_period() == period. The first period - 1 inputs are buffered while the seed accumulates; the period-th update() emits the simple average of those inputs as SMMA_period. Every later input applies the (prev·(n−1)+x)/n recurrence.

Edge cases

• Constant series. Feeding [7.0; n] returns Some(7.0) from input period onward — the recurrence is a fixed point for constants (constant_series_yields_the_constant pins this).
• NaN / infinity inputs. The first line of update is if !input.is_finite() { return self.current; }. Non-finite inputs are silently dropped — they neither advance the seed nor perturb the recurrence, and the previous valid value (if any) is returned.
• Reset. smma.reset() clears the seed buffer and the current value, restarting the warmup countdown.

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut smma = Smma::new(3)?;
    let out: Vec<Option<f64>> = smma.batch(&[1.0, 2.0, 3.0, 4.0, 5.0]);
    println!("{:?}", out);
    println!("warmup_period = {}", smma.warmup_period());
    Ok(())
}

Output:

[None, None, Some(2.0), Some(2.6666666666666665), Some(3.4444444444444446)]
warmup_period = 3

The third input emits the seed (1 + 2 + 3) / 3 = 2.0; the fourth applies (2.0·2 + 4) / 3 = 8/3; the fifth (8/3·2 + 5) / 3 = 31/9. This matches the warmup_then_recurrence test in crates/wickra-core/src/indicators/smma.rs.

Python

import numpy as np
import wickra as ta

smma = ta.SMMA(3)
print(smma.batch(np.array([1.0, 2.0, 3.0, 4.0, 5.0])))
print("warmup_period =", smma.warmup_period())

Output:

[      nan       nan 2.        2.6666667 3.4444444]
warmup_period = 3

Node

const ta = require('wickra');
const smma = new ta.SMMA(3);
console.log(smma.batch([1, 2, 3, 4, 5]));
console.log('warmupPeriod:', smma.warmupPeriod());

Output:

[ NaN, NaN, 2, 2.6666666666666665, 3.4444444444444446 ]
warmupPeriod: 3

Interpretation

Smma is a very smooth, lag-heavy price level. Because its smoothing factor is 1 / period rather than 2 / (period + 1), an Smma(n) is roughly as smooth as an Ema(2n − 1) — useful when you want maximum noise rejection from a single line. Its main role in this library, however, is structural: it is the exact smoothing kernel inside Rsi and Atr, so reaching for Smma directly lets you reproduce Wilder-style averages on any series.

Common pitfalls

• Confusing it with Ema at the same period. Smma(n) and Ema(n) are not interchangeable — Smma lags far more. Match Ema(2n − 1) if you need comparable smoothness.
• Treating period = 0 as "use a default". Smma::new(0) returns Err(Error::PeriodZero) in Rust and a ValueError in Python; pass an explicit period.

References

The smoothed moving average is J. Welles Wilder Jr.'s running average from New Concepts in Technical Trading Systems (1978); it is the averaging step in his RSI, ATR and ADX. The implementation here follows the standard SMA-seeded formulation, matching TA-Lib's RMA.

See also

• Indicator-Ema.md — faster exponential average.
• Indicator-Sma.md — the equal-weighted mean used as the SMMA seed.
• Indicator-Trima.md — the other F1 average.
• Indicators-Overview.md — the full taxonomy.