Inertia

Donald Dorsey's Inertia — a LinearRegression smoothing of his Relative Volatility Index (RviVolatility) of the close. The direction of volatility, smoothed into a trend gauge: above 50 bullish inertia, below 50 bearish.

Quick reference

Field	Value
Family	Momentum Oscillators
Input type	Candle (only the close is used)
Output type	f64
Output range	centred on 50; nominally 0–100 (the regression endpoint can overshoot slightly)
Default parameters	rvi_period = 14, linreg_period = 20
Warmup period	(2·rvi_period − 1) + linreg_period − 1 (46 for defaults)
Interpretation	Smoothed Relative Volatility Index; a cross of 50 signals a trend change.

Formula

Inertia_t = LinearRegression(RelativeVolatilityIndex(close, rvi_period), linreg_period)_t

RelativeVolatilityIndex (Dorsey 1993):
  sd_t    = stddev_pop(close over rvi_period)
  up_t    = sd_t if close_t > close_{t−1}, else 0
  down_t  = sd_t if close_t < close_{t−1}, else 0
  RVI_t   = 100 · Wilder(up) / (Wilder(up) + Wilder(down))     ∈ [0, 100]

Each bar's Relative Volatility Index value feeds a rolling least-squares regression; the endpoint of the fit is published. This is Dorsey's own construction (Technical Analysis of Stocks & Commodities, 1995) — it smooths the Relative Volatility Index, not the Relative Vigor Index (Rvi). Dorsey's thesis is that a market's inertia — its tendency to keep doing what it is doing — is best read from the smoothed direction of volatility rather than the noisy index itself. Although the input is a full Candle, only its close is used. See crates/wickra-core/src/indicators/inertia.rs.

Parameters

Name	Type	Default	Constraint	Source
rvi_period	usize	14	>= 1	Inertia::new (inertia.rs:48)
linreg_period	usize	20	>= 1	inertia.rs:48

Either parameter == 0 returns [Error::PeriodZero]. Inertia::classic() returns (14, 20). Python defaults come from #[pyo3(signature = (rvi_period=14, linreg_period=20))]; the Node constructor takes both explicitly. The public class is Inertia in both bindings.

Inputs / Outputs

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

• Python. update(candle) returns float | None; batch(open, high, low, close) returns an array.array('d') with NaN warmup. Only close affects the result; the other columns are still required (and validated) by the candle constructor.
• Node. update(open, high, low, close) returns number | null; batch(open, high, low, close) returns an Array<number> with NaN warmup.

Warmup

warmup_period() returns (2·rvi_period − 1) + linreg_period − 1. The inner Relative Volatility Index emits at 2·rvi_period − 1 candles (rvi_period to fill the standard-deviation window, overlapping by one bar with the rvi_period samples that seed the Wilder averages); the regression then needs linreg_period − 1 more values to fill its window. Classic (14, 20) → 46 (accessors_and_metadata). Pinned by warmup_emits_first_value_at_warmup_period ((3, 4) → warmup 8: first seven None, eighth emits).

Edge cases

• Constant close. Identical candles never move the close, so the Relative Volatility Index sits at its neutral 50 and the regression of a constant series equals that constant — Inertia reads exactly 50 (test constant_rvi_yields_constant_inertia).
• One-way market. A close that only rises saturates the index at 100 (only falls → 0), and Inertia follows it there.
• Zero period. Either period == 0 → Error::PeriodZero (rejects_zero_period).
• Reset. reset() resets both the inner Relative Volatility Index and the regression (reset_clears_state).

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut inertia = Inertia::classic(); // (14, 20)
    let mut last = None;
    for i in 0..80 {
        let o = 100.0 + f64::from(i);
        let c = o + 0.5;
        last = inertia.update(Candle::new(o, c + 0.2, o - 0.2, c, 1.0, i64::from(i))?);
    }
    println!("{last:?}");
    Ok(())
}

Output:

Some(100.0)

Every close is higher than the last, so the Relative Volatility Index saturates at 100 and the regression of that constant reads 100.

Python

import wickra as ta
inertia = ta.Inertia(14, 20)
out = inertia.batch(open_, high, low, close)  # 1-D series, NaN warmup (45 rows)

Node

const ta = require('wickra');
const inertia = new ta.Inertia(14, 20);
const v = inertia.update(100, 100.7, 99.8, 100.5); // open, high, low, close

Interpretation

Inertia is the Relative Volatility Index run through a regression smoother, so it trades responsiveness for stability:

1. Trend persistence. Above 50 ⇒ volatility is concentrated on up-bars ⇒ the market's "inertia" is bullish; below 50 ⇒ bearish. The slow smoothing makes the 50-line cross a higher-conviction trend-change signal than a raw Relative Volatility Index cross.
2. Pair with the raw index. Use raw RviVolatility for early reads and Inertia to confirm the trend has actually turned.

Common pitfalls

• Expecting raw-index-speed signals. Inertia deliberately lags — its warmup is (2·rvi_period − 1) + linreg_period − 1 bars (46 classic) and its turns trail the Relative Volatility Index's.
• Confusing the two RVIs. Inertia is built on Dorsey's Relative Volatility Index, not Ehlers' Relative Vigor Index (Rvi); the zero line is meaningless here — the neutral level is 50.
• Open, high and low ignored. Only the close is used; the other fields do not change the reading.

References

• Donald Dorsey, "Refining the Relative Volatility Index", Technical Analysis of Stocks & Commodities, 1995 — introduces Inertia.
• Donald Dorsey, "The Relative Volatility Index", Technical Analysis of Stocks & Commodities, June 1993.

See also

• RviVolatility — the underlying Relative Volatility Index.
• LinearRegression — the smoother applied.
• Rvi — the unrelated Relative Vigor Index.