Time-of-Day Return Profile

Mean bar return in each intraday time bucket. The local day is split into buckets equal slices and each bar's simple return is averaged into the bucket of its time-of-day.

Quick reference

Item	Value
Family	Seasonality & Session
Input type	Candle (uses close, timestamp)
Output type	TimeOfDayReturnProfileOutput { bins } (length buckets)
Output range	unbounded per bin (typically small)
Default parameters	buckets = 24, utc_offset_minutes = 0
Warmup period	2
Interpretation	Intraday return seasonality curve

Formula

bucket = floor(minute_of_day * buckets / 1440)   (clamped to buckets-1)
ret_t  = close_t / close_{t-1} - 1
bins[b] = mean of ret over bars whose bucket == b   (0.0 if empty)

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

Parameters

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

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

Inputs / Outputs

const _: fn(&mut wickra::TimeOfDayReturnProfile, wickra::Candle) -> Option<wickra::TimeOfDayReturnProfileOutput> =
    <wickra::TimeOfDayReturnProfile 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. The first bar produces no output (no return yet); from the second bar onward the full profile is reported each bar.

Edge cases

• Buckets by hour and means the returns (test buckets_by_hour_and_means_returns).
• Last bucket clamped for an end-of-day (23:59) bar (test last_bucket_clamped_for_end_of_day).
• Rejects buckets == 0 (test rejects_zero_buckets).
• Zero prior close uses a 0.0 return (test zero_prev_close_uses_zero_return).
• Reset clears all buckets (test reset_clears_state).

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let hour = 3_600_000;
    let mut prof = TimeOfDayReturnProfile::new(24, 0)?;
    prof.update(Candle::new(100.0, 100.0, 100.0, 100.0, 1.0, 0)?);            // 00:00, no return
    let out = prof.update(Candle::new(101.0, 101.0, 101.0, 101.0, 1.0, hour)?).unwrap();
    println!("{}", out.bins[1]); // 0.01 (01:00 bucket)
    Ok(())
}

Python

import wickra as ta

HOUR = 3_600_000
prof = ta.TimeOfDayReturnProfile(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])  # 0.01

Node

const wickra = require('wickra');
const HOUR = 3_600_000;
const prof = new wickra.TimeOfDayReturnProfile(24, 0);
prof.update(100, 100, 100, 100, 1, 0);
console.log(prof.update(101, 101, 101, 101, 1, HOUR)[1]); // 0.01

Streaming

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

Interpretation

1. Intraday seasonality map. Reveals systematically strong/weak times of day (e.g. open and close drift) — the basis for time-of-day entry filters.
2. Execution timing. Avoid placing passive orders in buckets with adverse mean drift.

Common pitfalls

• Bar spacing vs buckets. Choose buckets consistent with your bar interval; 24 buckets on 5-minute bars groups twelve bars per bucket.
• Survivorship. Means are unweighted across days; a few extreme days can dominate a thinly-populated bucket early on.

See also

• IntradayVolatilityProfile — volatility, not mean.
• VolumeByTimeProfile — volume by time.
• SeasonalZScore — normalised hourly anomaly.
• Indicators-Overview — full taxonomy.