F13b: add True Range, Chaikin Volatility, Z-Score and Linear Regression Angle
Second half of the eight indicators that fill out the new family taxonomy. - Rust core: true_range.rs (TrueRange — the raw single-bar volatility ATR averages), chaikin_volatility.rs (ChaikinVolatility — rate of change of a smoothed high-low spread), z_score.rs (ZScore — price normalised against its rolling mean and standard deviation) and linreg_angle.rs (LinRegAngle — the rolling regression slope as a degree angle). Each with a full Indicator impl, runnable doctest and reference / property / warmup / reset / batch==streaming tests. - Python / Node / WASM: classes wired through all three bindings (ZScore and LinRegAngle ride the scalar macros where possible) plus .pyi stubs and __init__.py / __all__ entries. - Wiki: four new Indicator-*.md pages. The eight-family taxonomy restructure (Overview / Home / README / folder layout) lands next in F13c. cargo fmt + clippy (core/wickra/data/wasm/node) clean; 508 core tests, 25 data tests and 74 doctests green.
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# LinRegAngle
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> Linear Regression Angle — the slope of the rolling least-squares fit,
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> expressed as an angle in degrees.
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## Quick reference
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| Field | Value |
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|-------|-------|
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| Family | Price Statistics |
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| Input type | `f64` (price) |
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| Output type | `f64` |
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| Output range | `(−90°, +90°)` |
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| Default parameters | `period = 14` (Python) |
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| Warmup period | `period` |
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| Interpretation | Steepness of the trend; sign is direction, magnitude is pitch. |
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## Formula
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```
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LinRegAngle = atan(LinRegSlope) · 180 / π
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```
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The angle carries exactly the same information as
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[`LinRegSlope`](Indicator-LinRegSlope.md) — positive while price trends up,
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negative while it trends down — but maps the unbounded slope through `atan`
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onto `(−90°, +90°)`. That bounded, price-unit-free scale makes "how steep is
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the trend" comparable at a glance and across instruments. This is TA-Lib's
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`LINEARREG_ANGLE`.
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## Parameters
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`period` — the regression window. Must be at least `2` (a line needs two
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points). The Python binding defaults it to `14`; the Rust and Node
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constructors require it explicitly.
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## Inputs / Outputs
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From `crates/wickra-core/src/indicators/linreg_angle.rs`:
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```rust
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impl Indicator for LinRegAngle {
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type Input = f64;
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type Output = f64;
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// update(&mut self, input: f64) -> Option<f64>
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}
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```
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`LinRegAngle` is a **scalar** indicator: it consumes one `f64` price per step.
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Because `Input = f64` it can sit inside a [`Chain`](../../Indicator-Chaining.md).
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## Warmup
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`LinRegAngle::new(14).warmup_period() == 14`. The first value lands once the
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window holds a full `period` prices.
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## Edge cases
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- **`period < 2`.** Rejected at construction — a regression line is undefined
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for fewer than two points.
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- **Unit slope.** A series rising by exactly `1` per step has slope `1`, and
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`atan(1) = 45°`.
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- **Flat series.** A constant input has slope `0` and therefore angle `0`.
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- **Reset.** `angle.reset()` clears the rolling regression window.
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## Examples
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### Rust
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```rust
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use wickra::{BatchExt, Indicator, LinRegAngle};
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fn main() -> Result<(), Box<dyn std::error::Error>> {
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let mut angle = LinRegAngle::new(5)?;
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// Closes rising by 1 per step -> slope 1 -> atan(1) = 45 degrees.
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let out = angle.batch(&[1.0, 2.0, 3.0, 4.0, 5.0, 6.0]);
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println!("{:?}", out);
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Ok(())
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}
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```
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Output:
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```
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[None, None, None, None, Some(45.0), Some(45.0)]
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```
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### Python
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```python
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import numpy as np
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import wickra as ta
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angle = ta.LinRegAngle(5)
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print(angle.batch(np.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0])))
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```
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Output:
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```
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[ nan nan nan nan 45. 45.]
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```
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### Node
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```javascript
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const ta = require('wickra');
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const angle = new ta.LinRegAngle(5);
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console.log(angle.batch([1, 2, 3, 4, 5, 6]));
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```
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Output:
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```
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[ NaN, NaN, NaN, NaN, 45, 45 ]
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```
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## Interpretation
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The angle is read like a slope: sign gives trend direction, magnitude gives
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how steeply price is pitched. Because it is bounded to `±90°` it is convenient
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for thresholds — e.g. "only trade with the trend while the angle exceeds
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`30°`" — and for comparing trend pitch across instruments with different price
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scales, which the raw [`LinRegSlope`](Indicator-LinRegSlope.md) cannot do.
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## Common pitfalls
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- **Reading degrees as a price quantity.** The angle depends on the chart's
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implicit scaling; treat it as a relative steepness gauge, not an absolute.
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- **Tiny periods.** `period = 2` reduces the fit to the last difference.
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## References
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The angle of an ordinary least-squares fit to a rolling price window; matches
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TA-Lib's `LINEARREG_ANGLE`.
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## See also
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- [Indicator-LinRegSlope.md](Indicator-LinRegSlope.md) — the same fit's slope,
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in raw price-per-bar units.
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- [Indicator-LinearRegression.md](Indicator-LinearRegression.md) — the
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endpoint of the same rolling fit.
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- [Indicators-Overview.md](../../Indicators-Overview.md) — the full taxonomy.
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# ZScore
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> Z-Score — how many standard deviations the latest price sits from its
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> rolling mean.
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## Quick reference
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| Field | Value |
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|-------|-------|
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| Family | Price Statistics |
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| Input type | `f64` (price) |
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| Output type | `f64` |
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| Output range | unbounded around zero (standard deviations) |
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| Default parameters | `period = 20` (Python) |
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| Warmup period | `period` |
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| Interpretation | Large magnitude = stretched; a return toward `0` = reversion. |
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## Formula
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```
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ZScore = (price − SMA(price, n)) / population_stddev(price, n)
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```
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The Z-Score normalises price against its own recent behaviour: it subtracts
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the rolling mean and divides by the rolling population standard deviation. A
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reading of `+2` means price is two standard deviations above its `n`-bar
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average — statistically stretched to the upside; `−2` is the mirror. It is the
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standard input to mean-reversion strategies.
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## Parameters
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`period` — the rolling window for the mean and standard deviation. The Python
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binding defaults it to `20`; the Rust and Node constructors require it.
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## Inputs / Outputs
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From `crates/wickra-core/src/indicators/z_score.rs`:
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```rust
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impl Indicator for ZScore {
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type Input = f64;
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type Output = f64;
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// update(&mut self, input: f64) -> Option<f64>
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}
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```
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`ZScore` is a **scalar** indicator: it consumes one `f64` price per step.
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Because `Input = f64` it can sit inside a [`Chain`](../../Indicator-Chaining.md).
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## Warmup
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`ZScore::new(20).warmup_period() == 20`. The first value lands once the window
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holds a full `period` prices.
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## Edge cases
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- **Zero dispersion.** A flat window has a zero standard deviation; `ZScore`
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is defined as `0` rather than dividing by zero.
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- **Rising series.** A monotonically rising price always scores above its
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trailing mean (positive).
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- **Reset.** `z.reset()` clears the rolling window.
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## Examples
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### Rust
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```rust
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use wickra::{BatchExt, Indicator, ZScore};
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fn main() -> Result<(), Box<dyn std::error::Error>> {
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let mut z = ZScore::new(2)?;
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// Window [1, 3]: mean 2, population stddev 1; latest 3 -> (3 - 2) / 1.
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println!("{:?}", z.batch(&[1.0, 3.0]));
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Ok(())
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}
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```
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Output:
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```
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[None, Some(1.0)]
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```
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### Python
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```python
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import numpy as np
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import wickra as ta
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z = ta.ZScore(2)
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print(z.batch(np.array([1.0, 3.0])))
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```
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Output:
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```
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[nan 1.]
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```
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### Node
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```javascript
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const ta = require('wickra');
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const z = new ta.ZScore(2);
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console.log(z.batch([1, 3]));
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```
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Output:
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```
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[ NaN, 1 ]
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```
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## Interpretation
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Z-Score is the workhorse of mean-reversion: a common rule enters against the
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move when `|ZScore| > 2` and exits as it crosses back through `0`. Read
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together with a trend filter — a high Z-Score in a strong trend is often
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continuation, not exhaustion, so the reversion edge is best in ranging
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regimes.
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## Common pitfalls
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- **Trading extremes blindly.** A trending market can hold a high Z-Score for
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a long time; pair it with a regime filter.
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- **Tiny periods.** A short window makes the mean and stddev jumpy.
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## References
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The standard statistical Z-Score (standard score) applied to a rolling price
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window.
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## See also
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- [Indicator-StdDev.md](../volatility/Indicator-StdDev.md) — the rolling
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standard deviation in the denominator.
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- [Indicator-LinearRegression.md](Indicator-LinearRegression.md) — another
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rolling statistical fit.
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- [Indicators-Overview.md](../../Indicators-Overview.md) — the full taxonomy.
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# ChaikinVolatility
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> Chaikin Volatility — the rate of change of a smoothed high-low spread;
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> is the trading range widening or narrowing?
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## Quick reference
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| Field | Value |
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|-------|-------|
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| Family | Volatility & Bands |
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| Input type | `Candle` (uses `high`, `low`) |
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| Output type | `f64` |
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| Output range | unbounded around zero (percent) |
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| Default parameters | `ema_period = 10`, `roc_period = 10` (Python) |
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| Warmup period | `ema_period + roc_period` |
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| Interpretation | Positive = ranges expanding, negative = ranges contracting. |
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## Formula
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```
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spread_t = high_t − low_t
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smoothed_t = EMA(spread, ema_period)_t
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ChaikinVol = 100 · (smoothed_t − smoothed_{t−roc_period}) / smoothed_{t−roc_period}
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```
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Marc Chaikin's volatility measure tracks not the *level* of the trading range
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but how fast it is *widening or narrowing*. The bar's high-low spread is
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EMA-smoothed, then run through a rate-of-change: a rising value means ranges
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are expanding (often near a market top, as fear spikes), a falling value means
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they are contracting (a quiet, complacent market). The classic configuration
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smooths the spread with a `10`-period EMA and takes its `10`-period rate of
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change.
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## Parameters
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- `ema_period` — the EMA that smooths the high-low spread (`10`).
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- `roc_period` — the rate-of-change lookback over the smoothed spread (`10`).
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`ChaikinVolatility::classic()` returns the `(10, 10)` configuration.
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## Inputs / Outputs
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From `crates/wickra-core/src/indicators/chaikin_volatility.rs`:
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```rust
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impl Indicator for ChaikinVolatility {
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type Input = Candle;
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type Output = f64;
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// update(&mut self, input: Candle) -> Option<f64>
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}
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```
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`ChaikinVolatility` is a **candle-input** indicator that reads `high` and
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`low`. Python's streaming `update` accepts a 6-tuple or a dict; the batch
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helper takes `high`, `low` numpy arrays. Node and WASM expose
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`update(high, low)` and the matching `batch`.
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## Warmup
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`ChaikinVolatility::classic().warmup_period() == 20`. The EMA emits at candle
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`ema_period`; the rate-of-change then needs `roc_period` more smoothed values.
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## Edge cases
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- **Constant range.** A constant high-low spread smooths to a constant EMA,
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whose rate of change is `0`.
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- **Expanding range.** A monotonically widening range reads positive.
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- **Reset.** `cv.reset()` clears the inner EMA and ROC.
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## Examples
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### Rust
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```rust
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use wickra::{BatchExt, Candle, Indicator, ChaikinVolatility};
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fn main() -> Result<(), Box<dyn std::error::Error>> {
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let mut cv = ChaikinVolatility::new(10, 10)?;
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// A constant 2-wide range -> constant EMA -> zero rate of change.
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let candles: Vec<Candle> = (0..40)
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.map(|i| {
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let base = 100.0 + f64::from(i);
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Candle::new(base, base + 1.0, base - 1.0, base, 1.0, i).unwrap()
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})
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.collect();
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println!("{:?}", cv.batch(&candles).last().unwrap());
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Ok(())
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}
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```
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Output:
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```
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Some(0.0)
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```
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### Python
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```python
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import numpy as np
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import wickra as ta
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cv = ta.ChaikinVolatility(10, 10)
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n = 40
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base = np.arange(n, dtype=float) + 100.0
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print(cv.batch(base + 1.0, base - 1.0)[-1])
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```
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Output:
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```
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0.0
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```
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### Node
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```javascript
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const ta = require('wickra');
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const cv = new ta.ChaikinVolatility(10, 10);
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const base = Array.from({ length: 40 }, (_, i) => 100 + i);
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const out = cv.batch(base.map((b) => b + 1), base.map((b) => b - 1));
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console.log(out[out.length - 1]);
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```
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Output:
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```
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0
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```
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## Interpretation
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A rising Chaikin Volatility warns that ranges are expanding fast — Chaikin
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associated sharp rises with market tops, where panic widens bars. A low or
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falling reading is the calm, range-contracting market that often precedes a
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move. It complements [`Atr`](Indicator-Atr.md): ATR gives the level of
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volatility, Chaikin Volatility gives its momentum.
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## Common pitfalls
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- **Reading it as a volatility level.** It is a *rate of change* — zero means
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steady ranges, not zero volatility.
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- **Feeding it scalar prices.** It needs the `high`/`low` bar.
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## References
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Marc Chaikin's Chaikin Volatility; the EMA-of-spread rate-of-change definition
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here is the standard one.
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## See also
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- [Indicator-Atr.md](Indicator-Atr.md) — the level of per-bar volatility.
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- [Indicator-TrueRange.md](Indicator-TrueRange.md) — raw single-bar range.
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- [Indicators-Overview.md](../../Indicators-Overview.md) — the full taxonomy.
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@@ -0,0 +1,147 @@
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# TrueRange
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> True Range — the single-bar volatility measure that ATR is the average
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> of, exposed raw.
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## Quick reference
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| Field | Value |
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|-------|-------|
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| Family | Volatility & Bands |
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| Input type | `Candle` (uses `high`, `low`, `close`) |
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| Output type | `f64` |
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| Output range | `[0, ∞)` (price scale) |
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| Default parameters | none (no parameters) |
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| Warmup period | `1` |
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| Interpretation | Per-bar volatility including overnight gaps. |
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## Formula
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```
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TR = max( high − low, |high − close_prev|, |low − close_prev| )
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```
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True Range is the greatest of the bar's own range and the two gaps to the
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previous close, so it captures volatility that opens *between* bars — an
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overnight gap — not only the range printed within a bar. The first bar has no
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previous close and falls back to `high − low`. Where [`Atr`](Indicator-Atr.md)
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is the Wilder-smoothed average of this series, `TrueRange` exposes it raw, one
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value per bar.
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## Parameters
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`TrueRange` takes **no parameters** — `TrueRange::new()` in Rust,
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`wickra.TrueRange()` in Python, `new ta.TrueRange()` in Node.
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## Inputs / Outputs
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From `crates/wickra-core/src/indicators/true_range.rs`:
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```rust
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impl Indicator for TrueRange {
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type Input = Candle;
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type Output = f64;
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// update(&mut self, input: Candle) -> Option<f64>
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}
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```
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`TrueRange` is a **candle-input** indicator that reads `high`, `low` and
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`close` (the close drives the gap terms). Python's streaming `update` accepts
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a 6-tuple or a dict; the batch helper takes `high`, `low`, `close` numpy
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||||
arrays. Node and WASM expose `update(high, low, close)` and the matching
|
||||
`batch`.
|
||||
|
||||
## Warmup
|
||||
|
||||
`TrueRange::new().warmup_period() == 1`. It emits a value from the very first
|
||||
candle — that bar simply has no previous close and uses `high − low`.
|
||||
|
||||
## Edge cases
|
||||
|
||||
- **First bar.** No previous close: `TR = high − low`.
|
||||
- **Gap.** A bar that opens far from the prior close has a `TR` larger than
|
||||
its own `high − low`.
|
||||
- **Non-negative.** `TR` is always `>= 0`.
|
||||
- **Reset.** `tr.reset()` drops the previous close; the next bar restarts.
|
||||
|
||||
## Examples
|
||||
|
||||
### Rust
|
||||
|
||||
```rust
|
||||
use wickra::{BatchExt, Candle, Indicator, TrueRange};
|
||||
|
||||
fn main() -> Result<(), Box<dyn std::error::Error>> {
|
||||
let mut tr = TrueRange::new();
|
||||
let out = tr.batch(&[
|
||||
Candle::new(11.0, 12.0, 8.0, 11.0, 1.0, 0)?, // no prev close -> 12 - 8
|
||||
Candle::new(9.5, 10.0, 9.0, 9.5, 1.0, 1)?, // prev close 11 -> max(1, 1, 2)
|
||||
]);
|
||||
println!("{:?}", out);
|
||||
Ok(())
|
||||
}
|
||||
```
|
||||
|
||||
Output:
|
||||
|
||||
```
|
||||
[Some(4.0), Some(2.0)]
|
||||
```
|
||||
|
||||
### Python
|
||||
|
||||
```python
|
||||
import numpy as np
|
||||
import wickra as ta
|
||||
|
||||
tr = ta.TrueRange()
|
||||
print(tr.batch(
|
||||
np.array([12.0, 10.0]), np.array([8.0, 9.0]), np.array([11.0, 9.5])
|
||||
))
|
||||
```
|
||||
|
||||
Output:
|
||||
|
||||
```
|
||||
[4. 2.]
|
||||
```
|
||||
|
||||
### Node
|
||||
|
||||
```javascript
|
||||
const ta = require('wickra');
|
||||
const tr = new ta.TrueRange();
|
||||
console.log(tr.batch([12, 10], [8, 9], [11, 9.5]));
|
||||
```
|
||||
|
||||
Output:
|
||||
|
||||
```
|
||||
[ 4, 2 ]
|
||||
```
|
||||
|
||||
## Interpretation
|
||||
|
||||
Read `TrueRange` as raw per-bar volatility. It spikes on wide-range or gapping
|
||||
bars and shrinks in quiet stretches. Smoothing it with a moving average gives
|
||||
[`Atr`](Indicator-Atr.md); using it directly is useful for volatility-scaled
|
||||
position sizing or for spotting single outlier bars an average would hide.
|
||||
|
||||
## Common pitfalls
|
||||
|
||||
- **Confusing it with `high − low`.** On a gap bar the True Range is larger —
|
||||
that is the whole point.
|
||||
- **Feeding it scalar prices.** It needs the full `high`/`low`/`close` bar.
|
||||
|
||||
## References
|
||||
|
||||
J. Welles Wilder Jr.'s True Range, from *New Concepts in Technical Trading
|
||||
Systems* (1978).
|
||||
|
||||
## See also
|
||||
|
||||
- [Indicator-Atr.md](Indicator-Atr.md) — the Wilder-smoothed average of the
|
||||
True Range.
|
||||
- [Indicator-ChaikinVolatility.md](Indicator-ChaikinVolatility.md) — a
|
||||
rate-of-change volatility measure.
|
||||
- [Indicators-Overview.md](../../Indicators-Overview.md) — the full taxonomy.
|
||||
Reference in New Issue
Block a user