Build Bars

Time bars sample by the clock, producing bars with wildly different information content - a 5-minute bar during the open contains 100x more trades than one at 2pm.

The Problem

Standard time bars (1-min, 5-min, daily) sample at fixed intervals regardless of market activity. During high-volume periods, a single bar compresses thousands of trades; during quiet periods, a bar may contain just a handful. This creates heteroscedastic returns that violate the i.i.d. assumptions of most ML models. Volume and dollar bars sample by activity instead, producing bars with roughly equal information content and returns closer to normality.

The Pattern

WRONG

import polars as pl

# Only using time bars - uneven information per bar
trades = pl.read_parquet("trades.parquet")
bars_5min = (
    trades.group_by_dynamic("timestamp", every="5m")
    .agg(
        open=pl.col("price").first(),
        close=pl.col("price").last(),
        volume=pl.col("size").sum(),
    )
)
# Bar at 9:30 has 5000 trades, bar at 14:00 has 50 trades

CORRECT

import numpy as np
import polars as pl

def bar_index(dollar_vol: np.ndarray, threshold: float) -> np.ndarray:
    """Bar id per trade: accumulate, close on the crossing, then RESET.

    Bucketing by the running total (cum_dollar // threshold) never resets, so
    an overshooting bar steals from the next: four $800 trades against a
    $1,000 threshold give $1,600, $800, $800, not two $1,600 bars."""
    idx = np.empty(len(dollar_vol), dtype=np.int64)
    bar, run = 0, 0.0
    for i, value in enumerate(dollar_vol):
        idx[i] = bar
        run += value
        if run >= threshold:
            bar, run = bar + 1, 0.0
    return idx

def build_dollar_bars(trades: pl.DataFrame, threshold: float) -> pl.DataFrame:
    """Build dollar bars: each bar contains ~threshold dollars traded."""
    trades = trades.sort("timestamp").with_columns(dollar_vol=pl.col("price") * pl.col("size"))
    return (
        trades
        .with_columns(bar_idx=bar_index(trades["dollar_vol"].to_numpy(), threshold))
        .group_by("bar_idx")
        .agg(
            timestamp=pl.col("timestamp").first(),
            open=pl.col("price").first(),
            high=pl.col("price").max(),
            low=pl.col("price").min(),
            close=pl.col("price").last(),
            volume=pl.col("size").sum(),
            dollar_volume=pl.col("dollar_vol").sum(),
            n_trades=pl.len(),
        )
        .sort("bar_idx")
    )

bars = build_dollar_bars(trades, threshold=1_000_000)  # $1M per bar

Choosing the Threshold

Calibrate the threshold as total dollar volume divided by the desired bar count.

Bar Type Comparison

Type	Samples On	Information Per Bar	Returns Distribution
Time	Clock interval	Uneven	Fat-tailed, heteroscedastic
Tick	N trades	More uniform	Closer to normal
Volume	N shares	Uniform for single stock	Good for single-name
Dollar	$N traded	Most uniform	Closest to normal

Guardrails

• Dollar bars require tick-level trade data (timestamp, price, size) - cannot build from OHLCV
• Thresholds are symbol-specific: $1M/bar for AAPL vs $50K/bar for a small-cap
• Volume and dollar bars are not directly comparable across symbols - normalize returns
• Overnight gaps should be handled (exclude or flag the first bar of each session)

Production Implementation

ml4t-engineer provides vectorized tick, volume, dollar, imbalance, and run-bar samplers:

from ml4t.engineer.bars import DollarBarSampler

bars = DollarBarSampler(dollars_per_bar=1_000_000).sample(trades.rename({"size": "volume"}))

Package-level names use vectorized implementations; compatibility implementations retain the Original suffix. Volume and imbalance samplers require a signed side column. Instantiate a concrete sampler with its class-specific threshold keyword, not the abstract BarSampler.

Checklist

• Tick data available with timestamp, price, and size columns
• Threshold calibrated to produce reasonable bar count (~same as time bars)
• Bars include OHLCV, dollar volume, and trade count
• Returns closer to normal verified (Jarque-Bera test or QQ plot)