wickra/docs/wiki/indicators/momentum/Indicator-Tsi.md

TSI

True Strength Index — a double-smoothed momentum oscillator that strips noise while keeping a clean, zero-centred read on trend pressure.

Quick reference

Field	Value
Family	Momentum
Sub-category	Unbounded oscillators
Input type	f64 (single close)
Output type	f64
Output range	roughly [−100, 100], centred on zero
Default parameters	(long = 25, short = 13) (Python)
Warmup period	long + short
Interpretation	Positive = net upward pressure, negative = net downward.

Formula

momentum_t = price_t − price_{t−1}
TSI = 100 · EMA_short(EMA_long(momentum)) / EMA_short(EMA_long(|momentum|))

The 1-bar momentum and its absolute value are each smoothed twice — first with an EMA of length long, then with an EMA of length short. The ratio of the two double-smoothed series normalises the result: when every recent move is up, numerator and denominator are equal and TSI saturates at +100; when every move is down, at −100.

Parameters

Name	Type	Default	Valid range	Description
long	usize	25 (Python)	>= 1	First (slow) smoothing length. 0 errors with Error::PeriodZero.
short	usize	13 (Python)	>= 1	Second (fast) smoothing length. 0 errors with Error::PeriodZero.

The Python binding defaults the pair to (25, 13) via #[pyo3(signature = (long=25, short=13))]. Node and WASM take both explicitly. The periods property returns (long, short).

Inputs / Outputs

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

impl Indicator for Tsi {
    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 / numpy.ndarray (NaN warmup); Node to number | null / Array<number> (NaN warmup).

Warmup

Tsi::new(long, short).warmup_period() == long + short. The momentum series starts on input 2; the SMA-seeded long EMA seeds at input long + 1, and the short EMA stacked on top seeds short − 1 inputs later, so the first non-None output lands on input long + short.

Edge cases

• Pure trend. A monotone rising series saturates at +100, a falling one at −100 — |momentum| equals momentum (or its negative), so the ratio is ±1 (pure_uptrend_saturates_at_plus_100 / pure_downtrend_saturates_at_minus_100 pin this).
• Constant series. Every momentum is 0; the 0 / 0 is guarded and the output is 0.0 (constant_series_yields_zero pins this).
• NaN / infinity inputs. Non-finite inputs are silently dropped; the smoothing chains are not advanced.
• Reset. tsi.reset() clears the previous price and all four EMAs.

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let prices: Vec<f64> = (1..=40).map(f64::from).collect();
    let mut tsi = Tsi::new(5, 3)?;
    let out = tsi.batch(&prices);
    println!("warmup_period = {}", tsi.warmup_period());
    println!("last = {:?}", out.last().unwrap());
    Ok(())
}

Output:

warmup_period = 8
last = Some(100.0)

A pure ramp has a constant +1 momentum, so the double-smoothed ratio is exactly 1 and TSI saturates at +100. This matches the pure_uptrend_saturates_at_plus_100 test in crates/wickra-core/src/indicators/tsi.rs.

Python

import numpy as np
import wickra as ta

tsi = ta.TSI()  # (long=25, short=13)
prices = np.linspace(100.0, 80.0, 60)  # steady downtrend
out = tsi.batch(prices)
print("last =", out[-1])

Output:

last = -100.0

Node

const ta = require('wickra');
const tsi = new ta.TSI(25, 13);
const prices = Array.from({ length: 60 }, (_, i) => 100 + i);
console.log('last:', tsi.batch(prices).at(-1));

Interpretation

Tsi is a low-noise momentum oscillator. The standard signals are the zero-line cross (momentum changing sign), overbought/oversold extremes near ±25 for the default settings, and a signal-line cross — many traders overlay an EMA of TSI and trade the crossover. The double smoothing makes divergences unusually clean compared with raw momentum.

Common pitfalls

• Reading it as a [0, 100] oscillator. TSI is centred on zero and signed; +25 is "strong up", not "mid-range".
• Under-budgeting warmup. Warmup is long + short — for the default (25, 13) that is 38 bars.

References

William Blau, "True Strength Index", Technical Analysis of Stocks & Commodities (1991), and Momentum, Direction, and Divergence (1995). The double-EMA-of-momentum definition here follows Blau's original.

See also

• Indicator-Mom.md — the raw momentum TSI smooths.
• Indicator-MacdIndicator.md — another EMA-difference momentum oscillator with a signal line.
• Indicators-Overview.md — the full taxonomy.