Intraday Volatility Profile

Return standard deviation in each intraday time bucket. The local day is split into buckets equal slices and each bar's simple return updates the per-bucket running variance (Welford); the reported value is the sample standard deviation.

Quick reference

Item	Value
Family	Seasonality & Session
Input type	Candle (uses close, timestamp)
Output type	IntradayVolatilityProfileOutput { bins } (length buckets)
Output range	>= 0 per bin
Default parameters	buckets = 24, utc_offset_minutes = 0
Warmup period	2
Interpretation	Intraday volatility seasonality (the "volatility smile")

Formula

bucket = floor(minute_of_day * buckets / 1440)   (clamped to buckets-1)
ret_t  = close_t / close_{t-1} - 1
bins[b] = sample std of ret over bars in bucket b   (0.0 if < 2 samples)

See crates/wickra-core/src/indicators/intraday_volatility_profile.rs.

Parameters

Name	Type	Default	Constraint	Source	Description
buckets	usize	24	> 0	intraday_volatility_profile.rs:43	Number of intraday slices.
utc_offset_minutes	i32	0	none	intraday_volatility_profile.rs:44	Shifts the instant before bucketing.

IntradayVolatilityProfile::new returns Error::PeriodZero for buckets == 0.

Inputs / Outputs

const _: fn(&mut wickra::IntradayVolatilityProfile, wickra::Candle) -> Option<wickra::IntradayVolatilityProfileOutput> =
    <wickra::IntradayVolatilityProfile as wickra::Indicator>::update;

• Python. update((o,h,l,c,v,ts)) → ndarray of length buckets (or None); batch(...) → (n, buckets) array, warmup rows NaN.
• Node. update(...) → number[] (or null); batch(...) → flat number[] length n*buckets.
• WASM. update(...) → Float64Array (or null).

Warmup

warmup_period() == 2. A bucket reports 0.0 until it holds at least two samples; the profile itself emits from the second bar onward.

Edge cases

• Single-sample bucket has zero volatility (test single_sample_bucket_has_zero_vol).
• Std matches a manual two-sample computation (test std_matches_manual_two_samples).
• Rejects buckets == 0 (test rejects_zero_buckets).
• Reset clears all buckets (test reset_clears_state).

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let hour = 3_600_000;
    let mut prof = IntradayVolatilityProfile::new(24, 0)?;
    prof.update(Candle::new(100.0, 100.0, 100.0, 100.0, 1.0, 0)?);
    let out = prof.update(Candle::new(101.0, 101.0, 101.0, 101.0, 1.0, hour)?).unwrap();
    println!("{}", out.bins[1]); // 0.0 (one sample in bucket 1)
    Ok(())
}

Python

import wickra as ta

HOUR = 3_600_000
prof = ta.IntradayVolatilityProfile(24, 0)
prof.update((100.0, 100.0, 100.0, 100.0, 1.0, 0))
out = prof.update((101.0, 101.0, 101.0, 101.0, 1.0, HOUR))
print(out[1])  # 0.0 until the bucket has two samples

Node

const wickra = require('wickra');
const HOUR = 3_600_000;
const prof = new wickra.IntradayVolatilityProfile(24, 0);
prof.update(100, 100, 100, 100, 1, 0);
console.log(prof.update(101, 101, 101, 101, 1, HOUR)[1]); // 0

Streaming

prof = ta.IntradayVolatilityProfile(48, -300)  # half-hourly, US Eastern
for o, h, l, c, v, ts in candle_feed:
    vol = prof.update((o, h, l, c, v, ts))
    # vol[b] is the running return std for intraday slice b

Interpretation

1. Volatility seasonality. Most markets show a "volatility smile" across the day — elevated at the open and close, quiet midday. This profile quantifies it.
2. Risk scheduling. Size positions and place stops with awareness of the bucket's typical volatility rather than a flat daily figure.

Common pitfalls

• Sample-vs-population std. Uses the unbiased sample standard deviation (n - 1); a bucket with one sample reports 0.0, not NaN.
• Bucket population. Thin buckets early in the history give unstable std estimates.

See also

• TimeOfDayReturnProfile — mean, not std.
• VolumeByTimeProfile — volume by time.
• HistoricalVolatility — rolling realised vol.
• Indicators-Overview — full taxonomy.