TrendStrengthIndex

Trend Strength Index — the signed coefficient of determination (r²) of a linear regression of price against time: how cleanly, and in which direction, the window trends.

Quick reference

Field	Value
Family	Trend & Directional
Input type	f64 (single price, usually the close)
Output type	f64
Output range	[-1, +1]; +1 clean uptrend, -1 clean downtrend, 0 flat/noisy
Default parameters	period is required
Warmup period (warmup_period())	period
Interpretation	Linear trend quality (r²), polarised by the regression slope.

Formula

regress y = close on x = 0..period-1
cov   = n·Σxy − Σx·Σy
r²    = cov² / [ (n·Σx² − (Σx)²)(n·Σy² − (Σy)²) ]
TSI   = sign(cov) · r²        (sign(cov) is the sign of the slope)

The coefficient of determination r² ∈ [0, 1] is the fraction of the price variance explained by a straight line over the window — a pure measure of how linear (trendy) the segment is, independent of direction. Multiplying by the slope's sign polarizes it into [-1, 1]: +1 is a perfectly straight uptrend, -1 a perfectly straight downtrend, and values near 0 mean the window has no linear structure (flat or noisy). A constant window (zero y-variance) has no defined trend and returns 0.

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

Parameters

Name	Type	Default	Valid range	Source	Description
period	usize	none	>= 2	trend_strength_index.rs:52	Regression window. 0 errors with Error::PeriodZero; 1 errors with Error::InvalidPeriod (a regression needs two points).

(Python class wickra.TREND_STRENGTH_INDEX(period); Node new ta.TREND_STRENGTH_INDEX(period).)

Inputs / Outputs

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

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

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

Warmup

warmup_period() returns period: the regression needs a full window before the first reading (bar period, index period − 1). Pinned by accessors_and_metadata (warmup_period() == 20) and warmup_emits_at_period.

Edge cases

• Perfect uptrend. perfect_uptrend_is_plus_one feeds a unit ramp; the fit is exact (r² = 1) with a positive slope → +1.
• Perfect downtrend. perfect_downtrend_is_minus_one feeds a falling ramp → -1.
• Flat market. flat_market_returns_zero: zero price variance → 0 (the var_y <= 0 guard).
• Noisy trend. noisy_trend_is_between: an upward drift with a sawtooth gives a positive reading strictly inside (0, 1).
• Reset. reset_clears_state empties the window buffer.
• Streaming/batch: batch_equals_streaming.

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut tsi = TrendStrengthIndex::new(10)?;
    // A clean ramp is a perfect uptrend -> r^2 = 1.
    let closes: Vec<f64> = (0..10).map(f64::from).collect();
    let last = tsi.batch(&closes).into_iter().flatten().last().unwrap();
    println!("{last}");
    Ok(())
}

Output:

1

A straight line fits the ramp exactly, so r² is 1 and the positive slope keeps the sign positive.

Python

import numpy as np
import wickra as ta

tsi = ta.TREND_STRENGTH_INDEX(10)
closes = np.arange(10, dtype=float)
out = tsi.batch(closes)   # NaN through warmup, then 1.0
print(out[-1])            # 1.0

Output:

1.0

Node

const ta = require('wickra');
const tsi = new ta.TREND_STRENGTH_INDEX(10);
let last = null;
for (let i = 0; i < 10; i++) last = tsi.update(i);
console.log(last); // 1

Output:

1

Streaming

use wickra::{Indicator, TrendStrengthIndex};

let mut tsi = TrendStrengthIndex::new(20)?;
let mut last = None;
for i in 0..60 {
    last = tsi.update(100.0 + (f64::from(i) * 0.2).sin() * 5.0);
}
println!("{last:?}");
# Ok::<(), Box<dyn std::error::Error>>(())

Interpretation

TSI answers "is there a trend, how strong, and which way?" in a single number:

1. Magnitude = trend quality. |TSI| near 1 means a clean, linear move; near 0 means no linear structure (range or noise).
2. Sign = direction. Positive is an uptrend, negative a downtrend.
3. Regime filter. Enable trend-following only when |TSI| is above a threshold (e.g. 0.5); fall back to mean-reversion when it is near zero.
4. Slope of TSI. A rising |TSI| means the trend is becoming more linear (strengthening); a falling one warns the move is breaking down into noise.

Common pitfalls

• It is not momentum. TSI measures linearity, not speed: a slow but perfectly straight drift scores ±1, while a fast but jagged move scores lower.
• Window sensitivity. r² is highly dependent on period; a short window finds local trends, a long one only the dominant one.
• Confusing it with the True Strength Index. This is a regression-r² trend gauge, unrelated to the momentum-based True Strength Index.

References

The coefficient of determination r² of ordinary least squares — the standard statistical measure of linear fit, applied here as a directional trend-strength gauge.

See also

• Indicator-LinearRegression — the fitted regression line itself.
• Indicator-ChoppinessIndex — a complementary trend-vs-range gauge.
• Indicators-Overview — the full taxonomy.