fugazi (Python)

Python bindings for fugazi, a library of incremental, composable technical-analysis primitives.

• Incremental — every indicator and signal carries its own state and is advanced one sample at a time with update(), in ~O(1) and with no full-history recomputation. The same object serves live streaming and batch backtesting.
• Composable — indicators own their input source, so you build complex indicators and signals by nesting constructors. There is no pipe or glue step: an "EMA of an SMA of the close" is literally ta.ema(ta.sma(ta.close(), 10), 20), and a trade condition is a single object you can feed bars.

Install

pip install fugazi

Then import fugazi. Prebuilt wheels are published for Linux, macOS (Intel + Apple Silicon) and Windows.

To build from a checkout instead (for development):

pip install maturin
maturin develop --release   # editable install into the active virtualenv

Quick start

You build indicators by nesting constructors. Every indicator is rooted at a leaf source — usually a candle field (close(), high(), volume(), ...):

import fugazi as ta

ema = ta.ema(ta.close(), 20)                  # EMA-20 of the close
node = ta.ema(ta.sma(ta.close(), 10), 20)     # EMA-20 of an SMA-10 — just keep nesting

The root decides what the indicator consumes. A candle-rooted indicator takes Candles (any of OHLCV); to work on a bare stream of numbers instead, root it at identity() — the leaf that passes raw values straight through:

prices = ta.rsi(ta.identity(), 14)            # RSI of a plain float series

Then drive it one of two ways: streaming (a bar at a time) or batch (a whole series at once). They share the same indicators; pick by how your data arrives.

What you feed update()/feed() follows from the root: a candle-rooted indicator consumes candles, an identity()-rooted one consumes plain numbers.

Streaming API — one sample at a time

Feed one sample to update(); it returns a float, or None until warmed up. This is the live/incremental path. Every node also has value() (or is_true() for a boolean Signal), is_ready(), and reset().

node = ta.ema(ta.sma(ta.close(), 10), 20)        # candle-rooted

for o, h, l, c, v in bars:
    value = node.update(ta.Candle(o, h, l, c, v))   # feed a Candle -> float | None
    print(value)

prices = ta.rsi(ta.identity(), 14)               # identity-rooted
for px in [100.0, 101.5, 100.8]:
    prices.update(px)                            # feed a float

Batch API — a whole series at once

feed(data) computes every bar in one call. For a candle-rooted indicator, data is a dataframe with OHLCV columns — pandas and polars both work (also a dict of columns) — and only the columns an indicator needs have to be present:

import pandas as pd      # or: import polars as pl

# df is your OHLCV frame (open/high/low/close/volume columns)
df["ema20"] = ta.ema(ta.close(), 20).feed(df)   # assigns straight back
ta.atr(14).feed(df)                             # uses high/low/close
ta.vwap(20).feed(df)                            # uses high/low/close/volume

Column names are matched case-insensitively (Close/CLOSE/close), and close is required. An identity()-rooted indicator instead takes a plain 1-D series — a list, NumPy array, or pandas/polars Series:

ta.ema(ta.identity(), 20).feed([100.0, 101.5, 100.8, 102.3, 101.9])
ta.ema(ta.identity(), 20).feed(df["close"])

(The root is the contract: a candle indicator won't silently treat a bare array as the close, and a value indicator won't accept a frame — pick the root that matches your data.)

The output mirrors the input library, one value per bar, with warm-up bars as NaN (so the result lines up with your rows and assigns straight back):

ta.ema(ta.close(), 20).feed(df)            # pandas Series, df.index
ta.macd(ta.close()).feed(df)               # pandas DataFrame: macd/signal/histogram
ta.macd(ta.identity()).feed(prices_list)   # {"macd": ndarray, "signal": ndarray, ...}

(If NumPy isn't installed, list/dict input falls back to plain Python lists.)

feed is itself incremental — it just loops update over the batch through the node's own state and never auto-resets. So calling it on successive chunks continues the same stream: the warm-up is paid once, and the concatenated outputs equal a single feed over the whole series. This is what lets you process data as it arrives without recomputing history:

node = ta.sma(ta.identity(), 3)
x1 = node.feed(series1)         # warms up, emits for series1
x2 = node.feed(series2)         # continues from where series1 left off
# np.concatenate([x1, x2]) == ta.sma(ta.identity(), 3).feed(series1 + series2)

node.reset()                   # call reset() to start a fresh, independent pass

A source can be reused after you pass it into a constructor:

src = ta.close()
fast = ta.ema(src, 10)
slow = ta.ema(src, 20)   # `src` is still usable here

Indicators

Multi-line indicators return a dict of their named lines (or None while warming up).

Projecting one line of a multi-output indicator: shared()

Call .shared() on any multi-output indicator (macd, bollinger, adx, donchian, keltner, dmi, aroon) to get a handle whose per-line accessors return ordinary Indicators that compose with the usual operators (gt, crosses_above, add, …). Every accessor built off one .shared() handle projects into the same underlying source — the multi advances at most once per bar however many accessors read out of it, exactly like Rust's Macd::new(...).shared():

# MACD line crossing its signal line, as a single composed Signal:
macd = ta.macd(ta.close(), 12, 26, 9).shared()
bullish = macd.line().crosses_above(macd.signal())

# Close pierces the Bollinger upper band:
bands = ta.bollinger(ta.close(), 20, 2.0).shared()
breakout = ta.close().gt(bands.upper())

The accessor names mirror the Rust API: line()/signal()/histogram() on a MACD, upper()/middle()/lower() on Bollinger/Keltner/Donchian, plus_di()/minus_di()/adx() on ADX/DMI, up()/down()/oscillator() on Aroon. component(name) is a programmatic fallback, names() lists what's available for a given handle. Calling .shared() returns a fresh handle owning its own copy of the source, so the original MultiIndicator (with its dict- returning .update() / .feed() API) stays usable in parallel.

Cross-timeframe composition

resample + latch compose a higher-timeframe pipeline over a base candle stream: resample(N, inner) aggregates every N base candles into one HTF candle and runs inner (any candle-rooted Real source — close(), ema(close(), 20), …) over it, emitting inner's output on the completing tick and None in between. The resample's clock stays base-timeframe: it's fed one base candle per update() and reports at that same cadence — the emitted output marks whether the inner produced a value on a completed bucket. Wrap the whole resample in latch() so per-base-tick reads see the finished value between boundaries.

# EMA-20 of the closes of every 4-bar candle, latched for per-base-tick reads.
htf_ema = ta.latch(ta.resample(4, ta.ema(ta.close(), 20)))

The only correct ordering is resample(N, ema(...)) — with the recursive smoother as the resample's inner — then latch on the outside; latching before the recursive smoother would feed it a held (repeated) value on every base tick, distorting the recurrence.

unstable(x) wraps an indicator or signal as a passthrough that reports unstable_period() = 0, telling a downstream reader of stable_period() (a strategy-readiness gate, an overlay trim) "trade through this subtree's IIR settling tail". Available as a free function and as a method on any Indicator or Signal — same output, same warm-up, only the reported unstable tail changes:

raw = ta.ema(ta.close(), 20)
fast = raw.unstable()           # method form; unstable_period() -> 0
fast = ta.unstable(raw)         # equivalent free-function form

Safe by default, override per subtree: fugazi's readiness machinery waits for stable_period() by default (SingleAssetStrategy::is_ready in Rust; the CLI's per-overlay CSV trim in fugazi get) — unstable(...) is the single opt-out.

Cross-asset composition — Snapshot, Selector, and pick(...)

To reason about more than one asset per bar, feed a Snapshot — a keyed collection of Atoms (one per asset for the current bar) — and use pick(...) to project one asset out of it. Every atom-input leaf (close(), high(), atr(), year(), is_weekday(), ...) takes an optional source= argument that re-roots it onto a pick(...), so cross-asset expressions compose from the same primitives as single-asset ones:

import fugazi as ta

# BTC's close as a first-class indicator over Snapshot input.
btc_close = ta.close(source=ta.pick("BTC"))

# BTC/ETH close spread — arithmetic between two picks is just an indicator.
spread = ta.close(ta.pick("BTC")) - ta.close(ta.pick("ETH"))

# Feed one snapshot per bar.
snap = ta.Snapshot({
    "BTC": ta.Atom(ta.Candle(100, 101, 99, 100, 1), time=1_710_504_000_000),
    "ETH": ta.Atom(ta.Candle(60, 61, 59, 60, 1),   time=1_710_504_000_000),
})
print(spread.update(snap))          # -> 40.0

Snapshot keys are Selectors — a (symbol?, freq?) pair. A Selector matches structurally: a None field on the query wildcards the corresponding storage field, so pick(symbol="BTC") finds every BTC entry regardless of frequency. A bare Python str is coerced to Selector.by_symbol(...), a (str, Frequency|str) tuple to a full (symbol, freq) pair, so most call sites don't need to reach for Selector explicitly. Cross-frequency indexes disambiguate by giving both fields:

snap = ta.Snapshot({
    ("BTC", "1h"): ta.Atom(ta.Candle(100, 101, 99, 100, 1), time=1_710_504_000_000),
    ("BTC", "1d"): ta.Atom(ta.Candle(90, 105, 88, 102, 1),  time=1_710_504_000_000),
    ("ETH", "1h"): ta.Atom(ta.Candle(60, 61, 59, 60, 1),    time=1_710_504_000_000),
})
btc_hourly = ta.close(ta.pick(symbol="BTC", freq="1h"))
any_hourly = ta.close(ta.pick(freq="1h"))              # wildcard on symbol
assert btc_hourly.update(snap) == 100.0

Snapshot behaves like a dict of atoms: snap[selector], snap[selector] = atom, selector in snap, len(snap), snap.keys(). Constructors accept a plain Python mapping, and update() accepts either a Snapshot or a bare dict (lifted on the fly), so the surface fits both "build the frame once" and "hand a fresh dict per bar" styles.

A pick(...) is atom-emitting, not real-emitting: it feeds any atom-input leaf via source=. Compositions preserve the input domain — the arithmetic below still consumes snapshots — and mixing a snapshot-rooted indicator with a candle-rooted one is a TypeError (a candle-input and a snapshot-input can't share a bar).

# Any atom-input leaf takes source=: the price accessors and every calendar
# reader, wired to the same picked atom stream.
btc_close = ta.close(source=ta.pick("BTC"))
btc_year  = ta.year(source=ta.pick("BTC"))
ratio     = ta.close(ta.pick("BTC")) / ta.close(ta.pick("ETH"))

The zero-arg pick() is the single-series shortcut. With no query it runs Snapshot.sole_atom on every bar: the snapshot must contain exactly one entry (its atom is what the pick emits), otherwise the call panics loudly (a Python RuntimeError translated from the Rust panic). That's the "strategy authored for one asset but fed a Snapshot-shaped driver" case — the loud failure catches multi-asset input that would otherwise silently pick whichever entry the HashMap iterator happened to hand back.

# Single-series strategy, snapshot-shaped input:
close = ta.close(source=ta.pick())
snap  = ta.Snapshot({"BTC": ta.Atom(ta.Candle(1, 1, 1, 42, 1))})
assert close.update(snap) == 42.0

Atom equality is by time. Two atoms compare equal iff their bar-open Timestamps match — the OHLCV numbers and overlays are payload, not identity — and atoms sort chronologically (None first), so mixed streams can be deduplicated by time and sorted into run order without a custom key:

a1 = ta.Atom(ta.Candle(1, 1, 1, 1, 0), time=1_000)
a2 = ta.Atom(ta.Candle(1, 1, 1, 99, 0), time=1_000)   # different price
a3 = ta.Atom(ta.Candle(1, 1, 1, 1, 0), time=2_000)
assert a1 == a2 and a1 < a3
assert len({a1, a2, a3}) == 2                          # a1 == a2, distinct from a3

Computing overlays — deriving columns from a series

A dataset is a series (bars) plus a set of overlays — derived columns computed from that series and carried on each bar's OverlayInfo side-channel. compute_overlays(series, overlays) runs the overlay indicators over the series and attaches the results, returning (schema, augmented). Read the columns back with get(...) — use the returned schema, the augmented atoms are bound to it:

import fugazi as ta

atoms = [ta.Atom(ta.Candle(c, c, c, c, 1_000)) for c in (10, 20, 30, 40)]

# `overlays` is a YAML doc of `name: !expr { ... }` ...
schema, out = ta.compute_overlays(atoms, "sma3: !sma { period: 3 }")
assert out[1].overlays.get_real(schema.index_of("sma3")) is None   # warming up
assert out[2].overlays.get_real(schema.index_of("sma3")) == 20.0   # mean(10,20,30)

# ... or a dict of pre-built indicators (Real / Signal → Bool / StrSource → Str).
schema, out = ta.compute_overlays(atoms, {"c": ta.close(), "hot": ta.close().above(15)})

reader = ta.get(schema, "c")            # resolve against the *returned* schema
assert [reader.update(a) for a in out][0] == 10.0

Existing overlay columns are preserved (same indexes) and the new columns appended, so overlays layer over a fetched series. A computed column reads None while it warms up. Snapshot sequences work too — each symbol's overlay derives from its own series, warming independently:

snaps = [
    ta.Snapshot({"BTC": ta.Atom(ta.Candle(b, b, b, b, 1)),
                 "ETH": ta.Atom(ta.Candle(e, e, e, e, 1))})
    for b, e in zip((10, 20, 30), (1, 2, 3))
]
schema, out = ta.compute_overlays(snaps, "sma3: !sma { period: 3 }")
assert out[2]["BTC"].overlays.get_real(schema.index_of("sma3")) == 20.0

Operators

Combine value indicators into other indicators:

ta.close().add(other)        # also: sub, mul, div  — or the + - * / operators
ta.close().lag(1)            # also: diff, ratio, roc
ta.close().rolling_max(20)   # also: rolling_min

...or into signals (booleans):

fast.gt(slow)                        # also: lt, ge, le, eq, ne  (optional epsilon=...)
ta.rsi(ta.close(), 14).above(70.0)   # also: below(level)
fast.crosses_above(slow)             # also: crosses_below

Signals compose with each other and update to a bool:

sig = a.and_(b)     # also: or_, xor_, not_(), changed()  — or  a & b | ~c
sig.update(candle)  # -> bool

Example

"Fast EMA crosses above slow EMA while RSI is not already overbought" — one signal, usable either way:

import fugazi as ta

def golden():
    return (
        ta.ema(ta.close(), 12)
          .crosses_above(ta.ema(ta.close(), 26))
          .and_(ta.rsi(ta.close(), 14).below(70.0))
    )

# streaming: react bar by bar
signal = golden()
for bar in stream:
    if signal.update(bar):
        print("entry signal")

# batch: a boolean Series/array over the whole frame
entries = golden().feed(df)

Trading: the wallet

The strategy layer is exposed two ways. For the classic single-asset shape there's a declarative Strategy builder you run over a wallet (below); for anything else, the wallet is a market-agnostic venue you trade into with your own per-bar Python — no class to subclass. PaperWallet is the built-in, in-memory book (funds + positions + a trade blotter); live execution belongs in your own code, not here.

import fugazi as ta

wallet = ta.PaperWallet(10_000.0)          # seed with cash

wallet.update("AAPL", 185.0)               # feed the price each tick (before trading)

# set: absolute target (opposite side reverses) · set_position: absolute units · close: flat
wallet.set("AAPL", "buy", 10)                       # target 10 units (a number = units)
wallet.set("AAPL", "buy", ta.Size.value_frac(0.25)) # target 25% of equity
wallet.set("AAPL", "buy", ta.Size.position_frac(0.5))  # trim to 50% of the position
wallet.set_position("AAPL", 4)                      # drive straight to 4 units
wallet.close("AAPL")                                # flatten

wallet.funds                 # cash balance
wallet.position("AAPL")      # signed position (negative = short)
wallet.price("AAPL")         # last fed price (or None)
wallet.positions()           # {symbol: units}
wallet.equity()              # funds + positions marked at the fed prices
wallet.orders()              # the blotter: list of Order(symbol, side, units)

The wallet is fed each symbol's price with update(symbol, price) and is otherwise market-agnostic. Sizes are an absolute number of units, or ta.Size.funds_frac(f) (cash) / ta.Size.value_frac(f) (equity; 1.0 is all-in) / ta.Size.position_frac(f); sides are "buy"/"sell". A movement that can't be carried out — no/zero price fed, or a buy beyond available funds — raises ValueError. A full strategy loop — price the wallet, advance every signal each bar, then act:

enter = ta.sma(ta.close(), 3).crosses_above(ta.sma(ta.close(), 10))
exit_ = ta.sma(ta.close(), 3).crosses_below(ta.sma(ta.close(), 10))
wallet = ta.PaperWallet(10_000.0)

for o, h, l, c, v in bars:
    candle = ta.Candle(o, h, l, c, v)
    wallet.update("AAPL", c)                          # price the wallet
    went_long, went_flat = enter.update(candle), exit_.update(candle)
    if went_long:
        wallet.set("AAPL", "buy", ta.Size.value_frac(1.0))   # all-in long
    elif went_flat:
        wallet.close("AAPL")

The declarative Strategy builder

For the classic long/flat/short shape, skip the hand-written loop: wire entry/exit signals (and an optional sizing multiplier) onto a Strategy and run it over a PaperWallet. You get back a RunReport — the per-bar equity curve and the fill blotter — that the metrics functions reduce to numbers.

import fugazi as ta
from fugazi.metrics import per_bar_returns, sharpe

enter = ta.sma(ta.close(), 3).crosses_above(ta.sma(ta.close(), 10))
exit_ = ta.sma(ta.close(), 3).crosses_below(ta.sma(ta.close(), 10))

strat = (
    ta.Strategy("AAPL")
    .long_on(enter, exit_)             # long/flat; add .short_on(down, up) for always-in
    .position_sizing(ta.value(0.5))    # optional: half-position (Kelly / vol-target fit here too)
)

prices = [10, 11, 12, 11, 10, 12, 14, 16, 15, 13, 15, 17, 19, 18]
ohlcv = {
    "open": prices,
    "high": [p + 1 for p in prices],
    "low": [p - 1 for p in prices],
    "close": prices,
    "volume": [1000.0] * len(prices),
}

wallet = ta.PaperWallet(10_000.0)
report = strat.run(wallet, ohlcv)      # a pandas/polars DataFrame or an OHLCV dict

report.equity_curve                    # one marked-to-market value per bar
report.fills                           # list[Fill] — the blotter, in fill order
rets = per_bar_returns(report.equity_curve, report.initial_equity)
sharpe(rets, 0.0, 252.0)

The builder mirrors Rust's SingleAssetStrategy: long_on / short_on (a missing exit never fires — right for an always-in reversal), position_sizing (scales the value-fraction magnitude; a None reading skips that bar's trade), and the strategy's book is seeded to the wallet's opening equity. Signals must be candle- or snapshot-rooted (a bare-value signal is rejected). Not bound yet: position-anchored protective stops and the Rust recipe catalogue — drop to the wallet loop above for those.

Portfolios

Portfolio runs N different strategies on one account, behind a single aggregate equity curve and blotter — the question none of the other shapes can answer. Children are ordinary Strategy / PairsStrategy / BasketStrategy / MultiAssetStrategy objects:

snapshots = [ta.Snapshot({"BTC": c, "ETH": c}) for c in stream]

# Root every leaf on the symbol it reads — see the note below.
btc, eth = ta.close(source=ta.pick("BTC")), ta.close(source=ta.pick("ETH"))

pf = (ta.Portfolio()
        .add("trend",  ta.Strategy("BTC").long_on(ta.ema(btc, 5).crosses_above(ta.ema(btc, 10)),
                                                  ta.ema(btc, 5).crosses_below(ta.ema(btc, 10))))
        .add("revert", ta.Strategy("ETH").long_on(ta.ema(eth, 5).crosses_below(ta.ema(eth, 10)),
                                                  ta.ema(eth, 5).crosses_above(ta.ema(eth, 10))))
        .weights([0.7, 0.3]))          # magnitudes; normalized, default equal

report = pf.run(ta.PaperWallet(10_000.0), snapshots)
report.equity_curve[-1]

Root your leaves. A portfolio always feeds children the full multi-symbol snapshot, so a bare ta.close() — which works in a standalone Strategy(...).run(wallet, candles), where each bar is a one-symbol frame — has no way to choose an asset here and raises. Wrap each leaf in ta.close(source=ta.pick(sym)), as the multi-symbol strategies below do.

Each child trades its own notional ledger — its slice of the account's cash and positions — and sizes against that, so value_frac(1.0) in a child still means all of that child's capital. Every child's intent is then netted into one order per symbol. Two consequences follow from sharing a book: children trading one symbol in opposite directions cross internally (and pay no spread or commission, because that part never traded), and a child's stop takes off only its own share.

The wallet passed to .run() is a cash seed only — a portfolio trades its own account, so costs installed on that wallet don't apply. .rebalance_on(sig) pulls capital back to the target weights when sig fires; without it the split drifts with P&L. Like the other builders it is immutable: .add(...) returns a new portfolio.

Not bound: live accounts (substrate) and per-child weight expressions — for those, write the portfolio as a portfolio: YAML document and use load_spec.

Multi-symbol strategies

PairsStrategy, MultiAssetStrategy and BasketStrategy mirror their Rust siblings and drive over a sequence of snapshots (.run(wallet, snapshots)). Their signals are snapshot-rooted, so atom leaves are rooted per symbol with ta.pick(sym).

PairsStrategy trades the spread close(left) − close(right), long / flat / short on it. long_spread_on goes long left / short right (profiting as the spread rises); short_spread_on is the mirror. A mean-reverting spread visits both tails and the correct position is opposite at each, so wiring only one side skips every excursion on the other:

spread = ta.close(ta.pick("BTC")).sub(ta.close(ta.pick("ETH")))
z = ta.zscore(spread, 60)

pair = (
    ta.PairsStrategy("BTC", "ETH")
    # spread cheap -> long it, close on reversion through 0
    .long_spread_on(z.lt(ta.value(-2.0)), z.gt(ta.value(0.0)))
    # spread rich -> short it (short BTC, long ETH)
    .short_spread_on(z.gt(ta.value(2.0)), z.lt(ta.value(0.0)))
)

The two directions are inverse positions, so they are mutually exclusive in time and share one capital pool at full notional; the opposite side's entry reverses an open pair. Per-side spread levels (long_spread_stop_loss / short_spread_stop_loss and the take-profit twins) compare with mirrored sense — the short side stops out when the spread rises above its level. on / spread_stop_loss / spread_take_profit remain valid as aliases for the long-spread side.

YAML strategy specs — load_spec, optimize, walkforward

The CLI's YAML surface (see the crate root's strategy.yml examples) is available natively from Python. ta.load_spec(text) parses a spec document, auto-detects its shape (single / pairs / basket / multi / portfolio), and returns a StrategySpec that implements the same .run(wallet, snapshots) interface as the manual Strategy builder. .evaluate(...) is a bonus method that runs + reduces to a metrics dict in one call.

import fugazi as ta

spec = ta.load_spec("""
symbol: BTC
long:
  enter: !crosses_above
    lhs: !sma { period: 3 }
    rhs: !sma { period: 10 }
""")
assert spec.kind == "single"

snaps = [
    ta.Snapshot({"BTC": ta.Candle(v, v, v, v, 1.0)})
    for v in [10, 9, 8, 7, 6, 7, 9, 12, 15, 18, 21, 22, 21, 20, 18, 15, 12, 10, 8, 6]
]
wallet = ta.PaperWallet(1000.0)
report = spec.run(wallet, snaps)              # -> RunReport
metrics = spec.evaluate(ta.PaperWallet(1000.0), snaps)  # -> nested dict mirroring metrics.yml

Pass windowed=N to .evaluate(...) for the same windowed/rolling reductions run -w N writes to metrics.csv/rolling.csv: the returned dict gains windowed (non-overlapping N-bar spans — independent, for cross-window statistics) and rolling (stride-1 spans — heavily autocorrelated, for a continuous rolling-Sharpe-style curve) keys, each a list of {"start_bar", "end_bar", "metrics"}. Unlike the CLI's -w, this takes a plain bar count — no duration/asset-class resolution.

Monte Carlo significance and the resampling primitive

Pass montecarlo=ta.MonteCarloConfig(...) to .evaluate(...) for the significance pass — bootstrap confidence intervals plus empirical-null p-values over a resampling scheme (iid / moving-block / stationary). The returned dict gains a montecarlo block (mirroring metrics.yml's), plus the raw per-resample metric values under montecarlo["samples"].

The significance layer reduces every resample to metric rows and discards the resampled paths. To draw a Monte Carlo equity fan chart (percentile bands of the resampled equity paths over time) you rebuild the paths yourself from one generic knob — the deterministic resampling index draws, exposed as fugazi.montecarlo:

resample_index_matrix(n, permutations, *, scheme="stationary", block=10.0, seed=0)
    -> list[list[int]]              # permutations × n, every index in 0..n
resample_indices(n, *, scheme="stationary", block=10.0, seed=0)
    -> list[int]                    # one sequence == permutation 0 of the matrix

The bootstrap-CI estimator draws first from the run's seed stream via the same primitive, so calling resample_index_matrix with n = len(returns) and the run's permutations/scheme/block/seed reproduces exactly the permutations behind the CIs. Every scheme yields a same-length synthetic series, so each rebuilt path is the same length as the source and maps 1:1 onto the original bar timestamps. Nothing large crosses a process boundary — you feed scalars and rebuild wherever you like:

import numpy as np
import fugazi as ta

spec = ta.load_spec("symbol: BTC\nlong:\n  enter: !crosses_above"
                    " { lhs: !sma { period: 3 }, rhs: !sma { period: 10 } }")
snaps = [ta.Snapshot({"BTC": ta.Candle(v, v, v, v, 1.0)})
         for v in [10, 9, 8, 7, 6, 7, 9, 12, 15, 18, 21, 22, 21, 20, 18, 15, 12, 10, 8, 6]]

rep = spec.run(ta.PaperWallet(1000.0), snaps)
r   = np.array(ta.metrics.per_bar_returns(rep.equity_curve, rep.initial_equity))
idx = np.array(ta.montecarlo.resample_index_matrix(
        len(r), 1000, scheme="stationary", block=10, seed=0))
paths = rep.initial_equity * np.cumprod(1 + r[idx], axis=1)   # (permutations × bars)
bands = {f"p{q}": np.percentile(paths, q, axis=0).tolist() for q in (5, 25, 50, 75, 95)}
spaghetti = paths[:200].tolist()                              # optional capped overlay

Bar k's band shares the time axis (position k ↔ times[k]) but is the k-th step of a synthetic return walk — a Monte Carlo fan, not a forecast conditioned on the real market at times[k].

Preset tags (!buy_and_hold, !ma_crossover, !rsi_reversal, !donchian_breakout, !keltner_breakout) work directly:

spec = ta.load_spec("!buy_and_hold { symbol: BTC }")

The five shapes are auto-detected by top-level YAML key:

Pass kind="single" / "pairs" / ... to override detection, and params={"NAME": value} to fill !param placeholders in the document.

Parameter-grid optimize

ta.optimize(text, snapshots, ...) sweeps a parameter grid, ranks rows by --best-by-style metric, and returns a Sweep:

spec_yaml = """
symbol: BTC
long:
  enter: !crosses_above
    lhs: !sma { period: !param FAST }
    rhs: !sma { period: !param SLOW }
"""
opt_snaps = [
    ta.Snapshot({"BTC": ta.Candle(v, v, v, v, 1.0)})
    for v in [100 + i * 0.5 for i in range(40)]
]

sweep = ta.optimize(
    spec_yaml,
    opt_snaps,
    cash=1000.0,
    grid=[{"FAST": [3, 5, 7], "SLOW": [10, 15]}],
    metric_names=["risk_adjusted.sharpe", "returns.total_pct"],
    best_by="risk_adjusted.sharpe",
)
sweep.columns          # -> ["FAST", "SLOW"]
sweep.rows[0].values   # -> {"FAST": 3, "SLOW": 10}
sweep.rows[0].metrics  # -> {"risk_adjusted.sharpe": ..., "returns.total_pct": ...}
sweep.best             # -> highest-ranked row (None when best_by is unset)

grid is a list of dicts (one per subgrid; stacked subgrids union), where values that are lists become sweep axes and "start..end[:step]" strings expand to numeric ranges. Pass windowed=N to reduce each grid point across non-overlapping N-bar windows (row.metrics_windowed carries the per-window docs), or walkforward=(is, oos) / walkforward=(is, oos, embargo) for walk-forward validation:

wf_yaml = """
symbol: BTC
long:
  enter: !crosses_above
    lhs: !sma { period: !param FAST }
    rhs: !sma { period: 15 }
"""
wf_snaps = [
    ta.Snapshot({"BTC": ta.Candle(v, v, v, v, 1.0)})
    for v in [100 + i * 0.5 for i in range(40)]
]

result = ta.optimize(
    wf_yaml,
    wf_snaps,
    cash=1000.0,
    grid=[{"FAST": [3, 5]}],
    best_by="risk_adjusted.sharpe",
    walkforward=(5, 3),
)
# -> WalkForwardResult with per-fold IS/OOS metrics + composite OOS equity
for fold in result.folds:
    fold.is_range, fold.oos_range     # bar ranges
    fold.values                         # winning params for that fold
    fold.is_metrics, fold.oos_metrics   # nested metrics dicts
result.composite_equity                 # stitched OOS curve
result.composite_metrics                # composite metrics doc

Costs

Trading costs load from a Python dict matching the CLI's YAML shape (externally-tagged models: !percentage, !bps, !volume_participation, …):

costs = ta.TradingCostsConfig({
    "commission": {"percentage": {"rate": 0.001}},
    "spread":     {"bps": {"bps": 5}},
})
cost_yaml = "!buy_and_hold { symbol: BTC }"
cost_snaps = [
    ta.Snapshot({"BTC": ta.Candle(v, v, v, v, 1.0)})
    for v in [100, 101, 102, 103, 104]
]
sweep = ta.optimize(cost_yaml, cost_snaps, cash=1000.0, grid=[{}], costs=costs)

Per-symbol / per-interval overrides use the same shape as the CLI:

costs = ta.TradingCostsConfig({
    "commission": {
        "default": {"percentage": {"rate": 0.001}},
        "by_symbol": {"BTC": {"percentage": {"rate": 0.0005}}},
    }
})

costs= accepts either a TradingCostsConfig or a raw dict on ta.optimize(...). For .run(wallet, snapshots) and .evaluate(wallet, snapshots), costs come from what's pre-installed on the wallet (matching how the manual Strategy builder works).

Metrics

fugazi.metrics is the standalone reporting surface — one function per metric so you pick only what you need. Return moments (mean_return, stddev_return, skewness, value_at_risk, …), risk-adjusted ratios (sharpe, sortino, calmar, omega, ulcer_performance_index), drawdown analytics (max_drawdown, average_drawdown, time_in_drawdown_ratio, recovery_factor), and round-trip trade statistics (win_rate, profit_factor, expectancy, kelly_fraction, average_bars_held, …) are all there. Values are in natural units — 0.15 is +15%, not 15.0 — and ratios that can vanish (zero variance for Sharpe, no losing trade for a profit factor, non-positive endpoints for CAGR) return None rather than NaN.

Three intermediate builders — per_bar_returns, reconstruct_trades, drawdown_segments — turn the equity curve and fill blotter into what the metric functions consume, so a caller computing several metrics builds each intermediate once:

from fugazi import metrics

equity = [10_000.0, 10_050.0, 10_100.0, 9_900.0, 10_200.0, 10_300.0]
returns = metrics.per_bar_returns(equity, initial_equity=10_000.0)

metrics.sharpe(returns, risk_free_rate=0.0, bars_per_year=252)   # ratio | None
metrics.total_return(equity, initial_equity=10_000.0)            # 0.03
metrics.max_drawdown(metrics.drawdown_segments(equity))          # fraction

reconstruct_trades walks a bar-tagged fill blotter with a signed position and a volume-weighted entry, producing one Trade per closed leg. Since PaperWallet.update() returns bare Orders (no bar), tag each with the bar you're on using fugazi.Fill(bar, order) as you drive the loop:

from fugazi import metrics

fills = []
wallet = ta.PaperWallet(10_000.0)
wallet.update("AAPL", candles[0])          # prime with a price for pre-flight
wallet.set_position("AAPL", 100.0)         # queued market buy
for i, c in enumerate(candles):
    for order in wallet.update("AAPL", c):
        fills.append(ta.Fill(bar=i, order=order))

trades = metrics.reconstruct_trades(fills)
metrics.win_rate(trades)                   # win fraction | None
metrics.profit_factor(trades)              # Σwins / |Σlosses| | None
metrics.exposure_ratio(fills, total_bars=len(candles))

Fetching data

Three remote candle providers ship built in — Binance and Okx (crypto spot klines) and Yahoo (stocks, ETFs, indices, FX). Each is a client class with one method, candles(...), returning a polars/pandas DataFrame (or a dict of lists with output="numpy"):

import fugazi as ta

binance = ta.Binance()                     # public endpoint, defaults
df = binance.fetch(symbol="BTCUSDT", freq="1d",
                   since="2020-01-01", until="today")

okx = ta.Okx()                             # symbols are dash-separated
df = okx.fetch(symbol="BTC-USDT", freq="1d", since="2020-01-01")

yahoo = ta.Yahoo()
df = yahoo.fetch(symbol="AAPL", freq="1d", since="2020-01-01")

freq is a bar-cadence token ("1m"/"5m"/"1h"/"4h"/"1d"/"1w"/"1M"); since/until accept ISO ("YYYY-MM-DD"), EU ("D-M-YYYY"), or relative ("today", "yesterday", "Nd ago", "Nw ago") dates, until is exclusive and defaults to now. The returned frame has time (ISO 8601 UTC), open, high, low, close, volume, and — carried through from each provider's own API — Binance's quote_volume, n_trades, taker_buy_base_volume, taker_buy_quote_volume; OKX's vol_ccy and quote_volume (its day/week/month bars are UTC-aligned). Yahoo candles are split/dividend-adjusted by default (ta.Yahoo(adjusted=False) to opt out): close is the adjusted price and the extra column is raw_close (the untouched close), or with adjusted=False the OHLCV are raw and the extra is adj_close.

fugazi.fetch(provider=..., symbol=..., ...) is the provider-generic form of the same call — handy when the provider name is itself a variable:

df = ta.fetch(provider="yfinance", symbol="AAPL", freq="1d", since="2020-01-01")

Overlay data (no OHLCV)

Every provider fetches through the same .fetch(...) method, but CoinGecko returns a different shape of frame: data that is a property of an asset at a point in time — market capitalisation, traded volume, supply — rather than a price bar. It carries no price, so the frame has no open/high/low/close (the OHLCV block is omitted whenever no row carries a bar):

cg = ta.CoinGecko()                        # public endpoint; COINGECKO_API_KEY if set
caps = cg.fetch(symbol="bitcoin", freq="1d", since="30d ago")
# columns: time, price, market_cap, total_volume, circulating_supply

symbol is a CoinGecko coin id ("bitcoin", not "BTC" and not "BTCUSDT"); cg.ids() lists the vocabulary. circulating_supply is derived as market_cap / price. To use these alongside prices, join the two frames on time — market cap and supply are not derivable from OHLCV at all, which is the whole reason the provider exists.

Two limits of the public tier: it serves only the last 365 days (a wider since raises ValueError), and sub-hourly frequencies are rejected, because CoinGecko only samples that finely over windows too short to backtest on. The provider-generic ta.fetch(provider="cg", ...) works too — it returns the same price-less frame.

BinanceVision is the same shape, for the perpetual funding rate — the periodic payment between the two sides of a perp (positive = longs pay shorts), the primary carry signal in crypto:

fund = ta.BinanceVision(market="futures")
rates = fund.fetch(symbol="BTCUSDT", freq="1d", since="90d ago")
# columns: time, funding_rate

symbol is a perpetual contract symbol, served from fapi.binance.com — a different host and listing set from the spot vocabulary Binance uses; fund.symbols() enumerates it.

Binance settles funding every 4–8 hours. Those are events, not bars, so a coarser freq covers several of them and their rates are summed: freq="1d" is that day's total carry, freq="8h" is one settlement per row. That is the right aggregation because funding is an accrual rather than a level (contrast CoinGecko's market cap, where the first sample in the bucket wins), and it means there is nothing to forward-fill — request the cadence you trade. Sub-hourly is rejected: those buckets would be empty on almost every bar, which reads as "no carry" rather than "no data". As with CoinGecko, ta.fetch(provider="binance-vision", ...) redirects rather than returning a candle-less frame.