ویژگی‌های مقاوم به نشت برای استراتژی‌های تأمین مالی قراردادهای آتی دائمی

# 03_financial_features.py


```py
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# %% [markdown]
# # Crypto Perps Funding: Feature Engineering
#
# A perpetual future has no expiry, so the only thing tying it to spot is a payment between its
# holders. That payment is the funding rate, and its sign says who pays whom: where the rate is
# positive the holders of long positions pay the holders of short ones, and where it is negative
# the payment runs the other way. What drives the sign is mostly how far the contract trades from
# spot, but not only that - the exchange adds a small interest term, so a contract trading a
# little below spot can still leave longs paying. It normally settles every eight hours, though
# the exchange can shorten an individual contract's interval, and Section B counts how often that
# happened here.
#
# What the exchange computes the rate from is the **premium index**, its own published measure of
# how far the contract sits from the spot price it tracks. Two things carry that name and this
# notebook uses only one of them: the funding formula takes a time-weighted average of the premium
# index over the interval ending at the settlement, and adds an interest term and a cap, while the
# features below read `premium_index_close`, the index's value at the close of each eight-hour
# bar. Every feature meant to rank one contract against another is a transformation of that series
# and of the settled rate; a handful of others describe the conditions a ranking is formed in and
# come from elsewhere - the contract's own price for its volatility, the timestamp for which of
# the three daily settlements a row belongs to, and the configuration for its fee tier. The
# question each feature has to answer first is not whether it predicts but whether it is knowable:
# at a settlement, which observations have already been published, and what does the feature make
# of them?
#
# ## Learning objectives
#
# - State a feature's timing contract - its lookback and its information lag - before writing the
#   code that computes it
# - Restamp a provider's bars from the time each one opened to the time it became knowable, and
#   see why every later shift, join and window inherits that single decision
# - Show that withholding later settlements leaves every feature value unchanged, which separates
#   a trailing statistic from one fitted over the whole sample
# - Read a feature set for scale, dispersion, redundancy and decay before any model sees it
#
# ## Book reference, prerequisites and artifacts
#
# Chapter 8. Reads eight-hourly perpetual bars and the premium index via `load_crypto_perps()`,
# the official Binance settlement series via `load_funding_rates()`, and `config/setup.yaml`.
# Writes `features/financial.parquet` with a `.digest.json` sidecar, read by
# [`04_model_based_features`](04_model_based_features.ipynb), which fits regime and volatility
# features on top of it fold by fold, and by [`05_evaluation`](05_evaluation.ipynb), which tests
# whether any of it predicts. [`02_labels`](02_labels.ipynb) stamps its forward returns the same
# way Section B stamps these features, so a feature row and a label row carrying one timestamp
# describe one decision; nothing here reads a label.

# %%
"""Crypto Perps Funding: Feature Engineering."""

from datetime import UTC, datetime, timedelta

import numpy as np
import polars as pl
import yaml
from IPython.display import display
from ml4t.engineer.features.ml import percentile_rank_features

from case_studies.crypto_perps_funding.funding_data import load_funding_rates
from case_studies.utils.artifact_digest import value_digest, write_artifact
from case_studies.utils.artifact_quality import (
    label_universe,
    quality_report,
    render_quality_report,
)
from case_studies.utils.feature_engineering import (
    EPS,
    assert_values_agree,
    assign_families,
    cross_sectional_percentile,
    families_from_config,
    family_coverage,
    plot_coverage_through_time,
    plot_cross_sectional_dispersion,
    plot_feature_distributions,
    plot_persistence,
    plot_redundancy_clusters,
    plot_timing_contract,
    register_frame,
    rolling_zscore,
    trailing_volatility,
    warmup_audit,
)
from case_studies.utils.warning_policy import apply_notebook_warning_policy
from data import load_crypto_perps
from utils.paths import get_case_study_dir

apply_notebook_warning_policy()

CASE_DIR = get_case_study_dir("crypto_perps_funding")
FEATURES_DIR = CASE_DIR / "features"

# %% [markdown]
# `START_DATE` is unset, so the loader below returns each perpetual's full history. Readers can
# override it through Papermill to run the notebook over a shorter window. There is no matching
# cap on the number of symbols: the within-settlement features rank each perpetual against the
# others trading at the same moment, and a truncated universe changes every one of those values.

# %% tags=["parameters"]
START_DATE = None

# %% [markdown]
# ## Configuration
#
# Every window, clip bound, the fee tier, the ranked column and the holdout boundary are declared
# in `config/setup.yaml` and bound here. A window typed into a cell is a second copy of a number
# the warmup audit and the timing figure both have to agree with, and the two drift apart the first
# time either is edited. Each window map reads `suffix: bars`: the emitted names carry hours in
# some families and days in others, and that naming is a schema every later stage reads.

# %%
setup = yaml.safe_load((CASE_DIR / "config" / "setup.yaml").read_text())
features_cfg = setup["features"]
FAMILIES = families_from_config(setup)
W = features_cfg["windows"]
CLIP = features_cfg["clip"]
MAJORS = set(features_cfg["majors"])
RANKED = features_cfg["ranked"]
REDUNDANCY_CUT = features_cfg["redundancy_cut"]
BAR_HOURS = features_cfg["bar_hours"]
BARS_PER_YEAR = setup["evaluation"]["periods_per_year"] * 24 / BAR_HOURS
HOLDOUT_START = datetime.fromisoformat(setup["evaluation"]["holdout_start"]).replace(tzinfo=UTC)
WINDOW_END = datetime.fromisoformat(setup["evaluation"]["holdout_end"]).replace(
    tzinfo=UTC
) + timedelta(days=1)

print(f"{len(FAMILIES)} declared families, {BAR_HOURS}-hour settlement bars")
print(f"Holdout opens {HOLDOUT_START.date()}; Section D rebuilds the panel without it")

# %% [markdown]
# ## A. What the thesis says should carry information
#
# The hypothesis is cross-sectional and it is about crowding. When a perpetual trades above the
# spot index, longs pay shorts to keep the contract open, and the size of that payment measures
# how one-sided the positioning is. A perpetual whose holders are paying most is expected to give
# ground relative to the rest of the universe over the following settlements. Three things follow.
#
# The **signal families** are funding and the premium it is computed from, entered in four
# representations rather than one, because a raw premium is comparable neither across symbols nor
# across regimes: the level, its z-score against its own history, its percentile within the
# settlement, and the speed at which it decays back. Which of those the effect lives in is a
# question `05_evaluation` asks.
#
# The **conditioning** is regime. Crowding unwinds differently in a quiet week than in a
# liquidation cascade - a stretch where falling prices force leveraged positions to be closed,
# which pushes prices down further and forces more of them - so the matrix also carries the
# dispersion of the premium and of the price, the
# short-over-long volatility ratios, a sustained-premium indicator and the settlement slot. These
# rank nothing against each other; they say which environment a ranking is being formed in, which
# is what the register's `role` column records and no assertion can recover from the values.
#
# The **failure modes** are stated with the families rather than discovered later: the exchange
# caps the funding rate at a fixed bound, so the rate stops moving in exactly the regimes that
# matter most, and momentum and mean reversion read one series with opposite signs, so a model
# given both may find they cancel. Every lag in the register is zero, and Section B is where that
# is earned.

# %%
register_frame(FAMILIES).select(["family", "role", "inputs", "lookback (bars)", "lag (bars)"])

# %% [markdown]
# ## B. Inputs and their observability
#
# Binance stamps each kline with the time its bar **opened**, so a row stamped midnight reports a
# close, a volume and a premium index that nobody knows until eight hours later. The series is
# advanced by one bar length before anything is joined, shifted or filtered, and the resulting
# `timestamp` is the boundary at which the completed bar is available.
# [`02_labels`](02_labels.ipynb) advances it the same way, so a feature row and a label row
# carrying one timestamp describe one decision.
#
# The official settlement series needs no such shift. Its `calc_time` is the settlement instant
# itself, and the rate is the time-weighted premium over the interval ending there plus the
# interest component and the exchange clamp - so the newest input to `funding_rate` at a
# timestamp is dated at that timestamp. The last two lines below are what would catch that being
# wrong: a rate determined by the interval that ends at its own stamp tracks the return over that
# interval, and a rate stamped a bar early would instead track the one that follows it.
#
# One feature is summed on the funding series' own clock rather than as a fixed number of rows on
# the eight-hour panel. Binance can shorten a contract's settlement interval to two or four hours
# when the premium runs far from its band, and during such a stretch seven days hold more than
# twenty-one settlements. A fixed twenty-one-row sum would then omit real cash flows, so the
# seven-day total is taken over a seven-day *time* window and counts whatever settlements fall in
# it. The count of shortened intervals printed below is how much of the sample this affects.

# %%
available_at = (pl.col("timestamp") + pl.duration(hours=BAR_HOURS)).alias("timestamp")
prices = (
    load_crypto_perps(frequency=f"{BAR_HOURS}h", start_date=START_DATE)
    .with_columns(available_at)
    .filter(pl.col("timestamp") < WINDOW_END)
    .sort(["symbol", "timestamp"])
)
funding = load_funding_rates(symbols=prices["symbol"].unique().to_list())
required = {"open", "high", "low", "close", "volume", "premium_index_close"}
assert not required - set(prices.columns), (
    f"loader missing {sorted(required - set(prices.columns))}"
)

cashflow_label, cashflow_days = next(iter(W["funding_cashflow"].items()))
cashflows = (
    funding.with_columns(pl.col("funding_rate").clip(lower_bound=0.0).alias("_paid"))
    .rolling(
        index_column="timestamp", period=f"{cashflow_days}d", group_by="symbol", closed="right"
    )
    .agg(pl.col("_paid").sum().alias(f"cum_positive_funding_{cashflow_label}"))
)
panel = prices.join(
    funding.select("timestamp", "symbol", "funding_rate"), on=["timestamp", "symbol"], how="left"
).join(cashflows, on=["timestamp", "symbol"], how="left")
observability = panel.sort(["symbol", "timestamp"]).select(
    pl.corr(pl.col("funding_rate"), pl.col("close").log().diff().over("symbol")).alias("backward"),
    pl.corr(
        pl.col("funding_rate"), pl.col("close").log().diff().over("symbol").shift(-1).over("symbol")
    ).alias("forward"),
)
print(f"{len(panel):,} settlement bars over {panel['symbol'].n_unique()} perpetuals")
print(f"{panel['funding_rate'].is_not_null().mean():.4%} of them carry an official settlement")
print(f"{funding.filter(pl.col('funding_interval_hours') != BAR_HOURS).height} shortened intervals")
print(f"funding against the interval it is computed from: {observability['backward'][0]:+.4f}")
print(f"funding against the interval that follows it:     {observability['forward'][0]:+.4f}")

# %% [markdown]
# ### What is actually in the panel
#
# The universe is a fixed list of nineteen perpetuals, and it is unbalanced: a contract enters the
# panel when Binance lists it and nothing is backfilled before that date. The table below carries
# the three properties of it that later sections here depend on, and
# [`01_feasibility_analysis`](01_feasibility_analysis.ipynb) describes the universe in full.
#
# **First settlement** is the earliest bar a contract contributes, and the spread of those dates is
# what makes the panel unbalanced - which is why C.5 normalizes its cross-sectional position by the
# number of contracts quoting rather than by a fixed nineteen. **Missing premium** counts the bars
# whose premium index the exchange did not publish; those are the gaps whose cost Section E
# measures, and they are not spread evenly across contracts. **Fee tier** is the `cost_tier_alt`
# feature, and it records an assumption rather than a measurement: the configuration assumes the
# five largest contracts can be traded passively, at the two-basis-point maker fee, and that the
# rest have to take liquidity at four. It reaches the matrix only as something a model can
# condition on. It does not set what a trade costs anywhere downstream - the backtest configuration
# charges one commission rate on every contract - so a difference between the two groups in the
# reported results comes from the model using the column, never from one group being charged more.

# %%
universe = (
    panel.group_by("symbol")
    .agg(
        pl.col("timestamp").min().dt.date().alias("first settlement"),
        pl.len().alias("bars"),
        pl.col("premium_index_close").is_null().sum().alias("missing premium"),
    )
    .with_columns(
        pl.when(pl.col("symbol").is_in(list(MAJORS)))
        .then(pl.lit("maker"))
        .otherwise(pl.lit("taker"))
        .alias("fee tier")
    )
    .sort(["first settlement", "symbol"])
)
with pl.Config(tbl_rows=universe.height, tbl_cols=universe.width):
    display(universe)

# %% [markdown]
# ## C. Feature construction, one subsection per family
#
# ### C.1 Carry: the funding rate and the premium it is computed from
#
# The z-score is the shared trailing primitive: mean and dispersion over the row's own history,
# divided by a dispersion held off zero by `EPS`, a small floor the case-study helpers apply so a
# window in which the series never moved returns a bounded number instead of dividing by zero. It
# does not rescue a window that has no dispersion to compute - one still filling, or one spanning
# a missing observation, is null before the floor and stays null after it. Its clip is not a guard
# but a decision the configuration declares, because a settlement-day outlier otherwise sets the
# scale a model reads.
#
# The half-life is local, since no library call covers it. It is the time a deviation in the
# settled rate takes to decay by half, read off a rolling AR(1) coefficient. That coefficient is
# the slope of a regression of the rate on its own previous value,
# $\rho = \mathrm{Cov}(r_t, r_{t-1}) / \mathrm{Var}(r_{t-1})$ - a slope, not a correlation, which
# would divide by both standard deviations instead. A series that decays geometrically at rate
# $\rho$ halves in $-\log 2 / \log|\rho|$ periods. Both moments are taken over trailing windows so
# nothing is estimated across the sample, and the result is clipped where the coefficient
# approaches one and the implied half-life diverges.
#
# Two choices in it are worth making explicit, because a reader building the same feature on their
# own data faces both. The first is that its denominator is guarded on being **positive** rather
# than floored at `EPS`. A floor is a guard only while it sits far below the quantity it protects,
# and that is a property of the units, not of the code: the denominator here is the variance of a
# rate whose typical magnitude is a basis point, so squaring it lands the whole distribution near
# the floor. The measurement below the definitions locates the floor against that distribution.
# Where it falls inside, flooring stops guarding and starts setting the answer, and a positivity
# test is what the guard should have been.
#
# The second is that a coefficient which cannot be estimated has no single sensible default, so
# each case is named rather than swept into one `otherwise`. Before the trailing moments exist
# there is no coefficient and the column is null. A coefficient of exactly zero is a series that
# has **already** reverted, so its half-life is the configured floor; the tempting alternative, to
# hand those rows the window length, reports the least persistent rows as the slowest to decay.


# %%
def carry_features(df: pl.DataFrame) -> pl.DataFrame:
    """Funding and premium level, dispersion-normalized, and the reversion speed."""
    z = CLIP["zscore"]
    df = df.with_columns(
        [
            rolling_zscore("premium_index_close", bars, "symbol")
            .clip(-z, z)
            .alias(f"premium_zscore_{label}")
            for label, bars in W["premium_zscore"].items()
        ]
        + [
            rolling_zscore("funding_rate", bars, "symbol")
            .clip(-z, z)
            .alias(f"funding_rate_zscore_{label}")
            for label, bars in W["funding_zscore"].items()
        ]
        + [pl.col("premium_index_close").alias("premium_level")]
    )
    for label, bars in W["funding_half_life"].items():
        df = funding_moments(df, bars).with_columns(
            half_life(bars, clip_variance=False, zero_to_window=False).alias(
                f"funding_half_life_{label}"
            )
        )
    return df.drop("_cov", "_var")


def funding_moments(df: pl.DataFrame, bars: int) -> pl.DataFrame:
    """Trailing covariance of the settlement series with its own lag, and the lag's variance."""
    lagged = pl.col("funding_rate").shift(1).over("symbol")
    return df.with_columns(
        (
            (pl.col("funding_rate") * lagged).rolling_mean(bars).over("symbol")
            - pl.col("funding_rate").rolling_mean(bars).over("symbol")
            * lagged.rolling_mean(bars).over("symbol")
        ).alias("_cov"),
        lagged.rolling_var(bars, ddof=0).over("symbol").alias("_var"),
    )


def half_life(bars: int, *, clip_variance: bool, zero_to_window: bool) -> pl.Expr:
    """Half-life implied by the trailing AR(1) coefficient, with two defects switchable.

    Neither flag reproduces a particular past revision; each reproduces a way this estimator
    can be wrong, so the cell below can assert against each rather than against a fixture
    written beside the fix.
    """
    floor, ceiling = CLIP["half_life"]
    if clip_variance:
        # A denominator floored rather than guarded: the clip stands in for a positivity test,
        # so a non-positive variance still divides and still yields a value rather than a null.
        rho = (pl.col("_cov") / pl.col("_var").clip(lower_bound=EPS)).clip(
            -CLIP["ar1"], CLIP["ar1"]
        )
    else:
        rho = (
            pl.when(pl.col("_var") > 0)
            .then(pl.col("_cov") / pl.col("_var"))
            .clip(-CLIP["ar1"], CLIP["ar1"])
        )
    if zero_to_window:
        # A near-zero coefficient routed to the window length, with the inner log clip that
        # kind of branch travels with.
        return (
            pl.when(rho.is_null())
            .then(None)
            .when(rho.abs() > 1 / bars)
            .then(-np.log(2) / rho.abs().log().clip(lower_bound=-10))
            .otherwise(pl.lit(float(bars)))
            .clip(floor, ceiling)
        )
    return (
        pl.when(rho.is_null())
        .then(None)
        .when(rho == 0)
        .then(pl.lit(floor))
        .otherwise(-np.log(2) / rho.abs().log())
        .clip(floor, ceiling)
    )


# %% [markdown]
# Whether `EPS` would work as the denominator's floor is a question about this panel's units, and
# it is cheaper to answer than to reason about. The trailing variance is compared against the floor
# directly: if the floor sits in the body of that distribution rather than below it, a floored
# denominator returns the floor on those rows and the half-life they report is a property of the
# constant, not of the rate. The same comparison is worth running on any series before reusing a
# shared epsilon on it: the same quantity expressed in percent and in basis points differs by four
# orders of magnitude once squared, and only one of the two clears a fixed floor.

# %%
_bars = W["funding_half_life"]["14d"]
_var = funding_moments(panel.sort(["symbol", "timestamp"]), _bars)["_var"]
_estimable = _var.drop_nulls()
print(f"denominator floor EPS:                        {EPS:.0e}")
print(f"median trailing variance of the settled rate: {_estimable.median():.2e}")
print(f"share of estimable rows below that floor:     {(_estimable < EPS).mean():.2%}")
print(f"share the positivity test rejects instead:    {(_estimable <= 0).mean():.2%}")


# %% [markdown]
# Neither branch is pinned by anything else in the notebook. The warmup audit and the seal both
# pass with the denominator floored again, or with a near-zero coefficient routed to the window
# length, so neither of them would notice the estimator changing underneath. A separate test file
# could only re-implement the expression, since the expression lives in this cell, and would then
# agree with whatever it was written beside.
#
# So both wrong versions stay reachable, as flags on the estimator, and the column the notebook
# emits is asserted against each of them over the whole panel. This is worth copying whenever a
# statistic is defined inside the notebook that uses it: a switch that reproduces the failure is a
# cheaper oracle than a fixture, and it stays true when the data changes. Each alternative is
# asserted separately, because a check that catches the two together does not say which one it
# caught.

# %%
_sorted = panel.sort(["symbol", "timestamp"])
# `now` is read out of `carry_features` rather than recomputed here. Recomputing it with the flags
# spelled out would make this cell agree with itself and pass however `carry_features` was edited.
_v = funding_moments(_sorted, _bars).select(
    carry_features(_sorted)["funding_half_life_14d"].alias("now"),
    half_life(_bars, clip_variance=True, zero_to_window=False).alias("eps_clipped"),
    half_life(_bars, clip_variance=True, zero_to_window=True).alias("both_defects"),
    ((pl.col("_var") > 0) & (pl.col("_var") < EPS)).alias("thin"),
)
_thin = _v.filter(pl.col("thin"))
_differs = (_thin["now"] - _thin["eps_clipped"]).abs() > 1e-9
# A warmup row has no coefficient to revert, so it cannot reach the window length by that branch.
# The share is taken over rows that have a coefficient, or the warmup would satisfy the check alone.
_estimated = _v.filter(pl.col("both_defects").is_not_null())
_at_window = (_estimated["both_defects"] == float(_bars)).mean()
assert (_v["now"] == float(_bars)).sum() == 0, "a reverted coefficient reports the window length"
assert _differs.mean() > 0.5, "the variance is being clipped: thin rows agree with the EPS oracle"
assert _at_window > 0.01, "no row reaches the window length carrying both defects"
print(f"variance positive but below the shared floor on {_v['thin'].mean():.2%} of rows")
print(f"  of those, {_differs.mean():.2%} would move if the denominator were floored there")
print(f"at the window length, of rows with a coefficient: {_at_window:.2%} with both, 0 now")


# %% [markdown]
# ### C.2 Mean reversion: where the premium sits in its own recent range
#
# The rolling percentile is `ml4t.engineer.features.ml.percentile_rank_features`, which ranks the
# current premium against the window that ends at it. It is a *time-series* percentile, not a
# cross-sectional one - it answers "high for this symbol lately", where C.5 answers "high against
# what everyone else is paying now" - and the two are separate features because they disagree
# whenever the whole universe moves together.


# %%
def mean_reversion_features(df: pl.DataFrame) -> pl.DataFrame:
    """Deviation from a trailing mean, position in the trailing distribution, sign persistence."""
    windows = W["premium_quantile"]
    ranks = percentile_rank_features(RANKED, windows=list(windows.values()))
    return df.with_columns(
        [
            (pl.col(RANKED) - pl.col(RANKED).rolling_mean(bars).over("symbol")).alias(
                f"premium_dev_mean_{label}"
            )
            for label, bars in W["premium_dev_mean"].items()
        ]
        + [
            ranks[f"rank_{bars}"].over("symbol").alias(f"premium_quantile_pos_{label}")
            for label, bars in windows.items()
        ]
        + [
            (pl.col(RANKED) > 0)
            .cast(pl.Float64)
            .rolling_mean(bars)
            .over("symbol")
            .alias(f"premium_persistence_{label}")
            for label, bars in W["premium_persistence"].items()
        ]
    )


# %% [markdown]
# ### C.3 Momentum: how the premium got where it is
#
# Six trailing differences, and two differences between them. The acceleration terms compare a
# short window against a longer one, so a premium that widened last settlement but has been
# narrowing all week reads differently from one doing both.


# %%
def momentum_features(df: pl.DataFrame) -> pl.DataFrame:
    """Premium differences at six horizons, the funding-rate change, and two accelerations."""
    horizons = W["premium_momentum"]
    df = df.with_columns(
        [
            (pl.col(RANKED) - pl.col(RANKED).shift(bars).over("symbol")).alias(
                f"premium_change_{label}"
            )
            for label, bars in horizons.items()
        ]
        + [
            (pl.col("funding_rate") - pl.col("funding_rate").shift(bars).over("symbol")).alias(
                f"funding_rate_change_{label}"
            )
            for label, bars in W["funding_change"].items()
        ]
    )
    short, medium, long = list(horizons)[1:4]
    return df.with_columns(
        (pl.col(f"premium_change_{short}") - pl.col(f"premium_change_{medium}")).alias(
            "premium_accel_short"
        ),
        (pl.col(f"premium_change_{medium}") - pl.col(f"premium_change_{long}")).alias(
            "premium_accel_medium"
        ),
    )


# %% [markdown]
# ### C.4 Volatility: two dispersions that are not the same quantity
#
# Price volatility is the shared trailing primitive on the perpetual's log return, annualized at
# the case study's own bar count so it is on the scale a volatility is read on and comparable with
# the other eight case studies. Premium volatility stays local and unannualized: the premium index
# is a rate in its own units rather than a return, so a root-time factor would put a number on it
# that does not mean what an annualized volatility means.


# %%
def volatility_features(df: pl.DataFrame) -> pl.DataFrame:
    """Trailing dispersion of the premium and of the price, plus short-over-long ratios."""
    df = df.with_columns(
        [
            pl.col("_premium_change").rolling_std(bars).over("symbol").alias(f"premium_vol_{label}")
            for label, bars in W["premium_volatility"].items()
        ]
        + [
            trailing_volatility(
                "_log_return", bars, "symbol", periods_per_year=BARS_PER_YEAR
            ).alias(f"price_vol_{label}")
            for label, bars in W["price_volatility"].items()
        ]
    )
    short, medium, long, longest = list(W["premium_volatility"])
    cap = CLIP["vol_ratio"]
    return df.with_columns(
        (pl.col(f"premium_vol_{short}") / pl.col(f"premium_vol_{long}").clip(lower_bound=EPS))
        .clip(upper_bound=cap)
        .alias("vol_ratio_short"),
        (pl.col(f"premium_vol_{medium}") / pl.col(f"premium_vol_{longest}").clip(lower_bound=EPS))
        .clip(upper_bound=cap)
        .alias("vol_ratio_medium"),
    )


# %% [markdown]
# ### C.5 Cross-sectional position within one settlement
#
# Three statistics taken with `.over("timestamp")`, so each reads every symbol trading at that
# settlement and no other date. The percentile uses the shared primitive, whose denominator is the
# count plus one: that keeps the widest-premium perpetual off the boundary, so the column is a
# position in the cross-section rather than a rank divided by its own maximum. That distinction is
# what makes it comparable across dates, and the table above is why it matters here - the panel is
# unbalanced, so an early settlement ranks a handful of contracts and a late one ranks nineteen,
# and a rank divided by its own maximum would put the widest premium at the top of the scale in
# both, whether it beat two contracts or eighteen.


# %%
def cross_sectional_features(df: pl.DataFrame) -> pl.DataFrame:
    """Distance from the settlement's median, its z-score, and the dispersion of funding paid."""
    return df.with_columns(
        (pl.col(RANKED) - pl.col(RANKED).median().over("timestamp")).alias("premium_vs_median"),
        (
            (pl.col(RANKED) - pl.col(RANKED).mean().over("timestamp"))
            / pl.col(RANKED).std().over("timestamp").clip(lower_bound=EPS)
        )
        .clip(-CLIP["zscore"], CLIP["zscore"])
        .alias("premium_xs_zscore"),
        pl.col("funding_rate").std().over("timestamp").alias("xs_funding_dispersion"),
    )


# %% [markdown]
# ### C.6 Regime and calendar
#
# The oscillator is the relative strength index: the share of recent movement that was upward,
# mapped onto a nought-to-hundred scale, so a premium that has only widened reads near a hundred
# and one that has only narrowed reads near nought. The library call
# `ml4t.engineer.features.momentum.rsi` is the standard form, and it is deliberately not used here.
# It carries Wilder's smoothing, a recursive average in which each value is computed from the one
# before it, and a recursion has no way to skip a missing observation: the premium index has gaps,
# and the first one a contract meets propagates into every value after it. An average over a fixed
# window has a defined answer in both cases - nothing while the window spans the gap, and a usable
# number once the gap has passed out of it. The two are different statistics rather than two
# implementations of one, which is why this column is not called a Wilder RSI.
#
# The settlement slot and the fee tier are the two columns with no lookback at all: the slot is a
# property of the timestamp, and the tier is a fixed list the configuration declares.


# %%
def regime_features(df: pl.DataFrame) -> pl.DataFrame:
    """Sustained-premium indicator, bounded oscillators, settlement slot and fee tier."""
    return df.with_columns(
        [
            pl.when(pl.col(RANKED) > 0)
            .then(1.0)
            .otherwise(-1.0)
            .rolling_mean(bars)
            .over("symbol")
            .alias(f"premium_regime_{label}")
            for label, bars in W["premium_regime"].items()
        ]
        + [
            (
                100
                - 100
                / (
                    1
                    + pl.col("_premium_change")
                    .clip(lower_bound=0)
                    .rolling_mean(bars)
                    .over("symbol")
                    / (-pl.col("_premium_change"))
                    .clip(lower_bound=0)
                    .rolling_mean(bars)
                    .over("symbol")
                    .clip(lower_bound=EPS)
                )
            ).alias(f"premium_rsi_{label}")
            for label, bars in W["premium_rsi"].items()
        ]
        + [
            (pl.col("timestamp").dt.hour() // BAR_HOURS).cast(pl.Int32).alias("funding_session"),
            pl.when(pl.col("symbol").is_in(list(MAJORS)))
            .then(0)
            .otherwise(1)
            .cast(pl.Int32)
            .alias("cost_tier_alt"),
        ]
    )


# %% [markdown]
# ### C.7 The order the three steps run in
#
# Everything above is computed from one perpetual's own history, so the order those steps run in
# does not matter. The four within-settlement statistics are different, and they put the null
# policy **between** the two groups rather than after both. A percentile, a median and a dispersion
# are properties of the cross-section they are taken over, so a perpetual the matrix will not carry
# must not be in that cross-section: leaving it in moves the number written for every perpetual
# that is. Gate first, then take the cross-section over exactly the rows that survived.
#
# That ordering decides which cross-section is read. It does not yet establish that there is one.
# The z-score and the dispersion are both standard deviations over the settlement, and a standard
# deviation is undefined at a single observation, so a settlement the gate reduces to one perpetual
# has no value to write for either. The gate therefore takes a second clause - a settlement reaches
# the matrix only if at least `MIN_CROSS_SECTION` perpetuals survive it - and the median and the
# percentile go with them, because a position in a cross-section of one is not a position at all.


# %%
def per_symbol_features(df: pl.DataFrame) -> pl.DataFrame:
    """Everything computed from one perpetual's own history, before any gate."""
    return (
        df.sort(["symbol", "timestamp"])
        .with_columns(
            (pl.col(RANKED) - pl.col(RANKED).shift(1).over("symbol")).alias("_premium_change"),
            pl.col("close").log().diff().over("symbol").alias("_log_return"),
        )
        .pipe(carry_features)
        .pipe(mean_reversion_features)
        .pipe(momentum_features)
        .pipe(volatility_features)
        .pipe(regime_features)
    )


# Two, because that is the smallest cross-section a standard deviation is defined on. This is not
# a tuning choice and it is not declared in the configuration for that reason.
MIN_CROSS_SECTION = 2


def build_features(df: pl.DataFrame) -> pl.DataFrame:
    """The whole construction, as one function Section D can re-run on a shorter panel."""
    trailing = per_symbol_features(df)
    eligible = trailing.drop_nulls(subset=[c for c in SYMBOL_COLS if c in trailing.columns])
    contested = eligible.filter(pl.len().over("timestamp") >= MIN_CROSS_SECTION)
    return contested.pipe(cross_sectional_features).with_columns(
        cross_sectional_percentile(RANKED, "timestamp").alias("premium_rank")
    )


# The two carry columns are joined in Section B and shipped as features, so they are added back
# to the input frame's own columns before the difference; taking the difference alone drops them.
CARRIED = {"funding_rate", f"cum_positive_funding_{cashflow_label}"}
EXCLUDED = (set(panel.columns) | {"_premium_change", "_log_return"}) - CARRIED
XS_COLS = ["premium_vs_median", "premium_xs_zscore", "xs_funding_dispersion", "premium_rank"]

trailing = per_symbol_features(panel)
SYMBOL_COLS = sorted(c for c in trailing.columns if c not in EXCLUDED)
built = build_features(panel)
feature_cols = sorted(assign_families(SYMBOL_COLS + XS_COLS, FAMILIES))
print(f"{len(trailing):,} bars carrying {len(SYMBOL_COLS)} per-symbol features")
print(f"{len(built):,} pass the gate and carry the {len(XS_COLS)} within-settlement features")

# %% [markdown]
# ## D. The timing contract
#
# ### D.1 What each construction reads
#
# Three kinds of operation appear above. A **rolling** window ends at its own row and reads a fixed
# number of settlements backward, always `.over("symbol")`, so a shift means "the previous
# settlement for this perpetual" and never "the previous row in the file". A **cross-sectional**
# statistic - the three in C.5 and the percentile - is taken with `.over("timestamp")`, so it reads
# every perpetual at that settlement and no other date. A **time-based rolling** aggregate builds
# the seven-day cash flow on the settlement series' own clock, which is what lets it span an
# interval the exchange shortened. None of the three reaches forward, and D.2 and D.3 establish it
# rather than asserting it. F4, below the coverage figure, draws the same contract as a picture.
#
# ### D.2 Warmup
#
# A trailing window cannot produce a value until it has enough settlements to fill, so every family
# has a leading stretch of nulls as long as its lookback. The audit checks that length rather than
# describing it: a column holding a value before its window could have filled is reading bars that
# do not exist, and that is what it raises on. It is worth running even where the windows look
# obvious, because the failure it catches is not a wrong window but a branch that returns a
# fallback instead of a null - a column that reports a value from the first bar of the sample has
# a default somewhere, and a default is indistinguishable from an estimate once it is in a model.
#
# It runs on the panel before the gate, because the gate drops the warmup stretch it measures.

# %%
warmup_audit(
    trailing,
    {
        "premium_change_720h": W["premium_momentum"]["720h"],
        "premium_quantile_pos_30d": W["premium_quantile"]["30d"],
        "premium_zscore_14d": W["premium_zscore"]["14d"],
        "funding_rate_zscore_14d": W["funding_zscore"]["14d"],
        "funding_half_life_14d": W["funding_half_life"]["14d"],
        "price_vol_14d": W["price_volatility"]["14d"],
        "premium_vol_336h": W["premium_volatility"]["336h"],
        "vol_ratio_medium": W["premium_volatility"]["336h"],
        "premium_regime_72h": W["premium_regime"]["72h"],
    },
    entity="symbol",
)

# %% [markdown]
# ### D.3 Withholding the holdout changes nothing
#
# Trailing and within-settlement statistics share a property worth checking directly: recomputed on
# a panel that stops before the holdout, they reproduce the same values on the rows the two panels
# share. A parameter fitted over a whole column - a winsorization bound, a scaler, an encoder -
# does not, because truncating the column moves the parameter and with it every row it was applied
# to. Building the panel twice tests the whole construction at once, every emitted column rather
# than a sample, and does not depend on anyone having flagged the transform that fits. A value on
# one side against a null on the other counts as a difference, which is the form of the failure a
# null-skipping comparison hides.

# %%
seal = assert_values_agree(
    built.filter(pl.col("timestamp") < HOLDOUT_START),
    build_features(panel.filter(pl.col("timestamp") < HOLDOUT_START)),
    columns=feature_cols,
    keys=["timestamp", "symbol"],
)
seal.filter(pl.col("column").is_in(["premium_rank", "premium_xs_zscore", "funding_half_life_14d"]))

# %% [markdown]
# ## E. Matrix assembly and coverage
#
# The panel key is `symbol` + `timestamp`. The raw open, high, low, close, volume and premium index
# are excluded: they are the inputs the features are made of, and a model handed the
# contemporaneous close beside a label derived from the same price would be reading its own answer.
# So are the two intermediates the construction passes between subsections. `premium_level` is the
# deliberate exception, the premium index under a name that says it is shipped as a signal.
#
# One null policy is applied once, and C.7 is where: a row reaches the matrix only when every
# per-symbol feature on it is observed and its settlement retains the two perpetuals a
# within-settlement statistic needs, and those statistics are then taken over exactly the rows that
# survived. Dropping a row is the strictest of the available policies and it is chosen deliberately:
# a model handed a null has to be told what to do with it, the successor stages include sequence
# models that have no answer, and the alternative - filling the gap with a carried-forward or
# imputed value - invents an observation the exchange never published. The assertion below is what
# makes the resulting matrix complete by fact rather than by intention.
#
# What that buys is that every row emitted is complete on every feature. What it does not buy is
# that the rows are consecutive: dropping a row leaves a hole in the settlement sequence. A model
# reading this matrix row by row - and the sequence models downstream do - forms a window by
# counting rows, so a window of sixty rows that spans a hole covers more than sixty settlements of
# elapsed time. That is a property of the emitted panel, and the timestamp column is what a
# consumer would have to read to detect it.
#
# That policy has a price, and it is worth knowing where the price is paid before reading the
# coverage figure. The perpetual close and its volume are complete. The other two inputs are not:
# the premium index has scattered gaps, and a small share of bars carry no official settlement,
# both of which Section B counts. One missing observation of either empties every window that
# spans it. How many rows that costs depends on
# the shape of the statistic: a rolling window of ninety settlements is spanned by ninety
# successive rows, so one gap removes ninety, while a difference against the value ninety
# settlements back reads only two rows and removes two. Gaps close together cost less than gaps
# far apart, because their invalidated stretches overlap - two gaps k settlements apart, with k
# below the window length, remove the window length plus k rows rather than twice the window - but
# they never cost nothing extra. And because a row is kept only when every feature on it is
# observed, it is the longest window in the matrix that sets the reach of each gap.
#
# The cell below splits the discarded rows between those gaps and the warmup, and it does so by
# measurement rather than by reasoning about which input feeds which feature. Each contract's
# first complete row is the boundary: anything dropped before it is that contract filling its
# windows after listing, and anything dropped after it was lost while the contract was already
# producing every feature, which only a missing input can do. The second figure is therefore an
# attribution by elimination rather than by inspection - it does not say which of the two inputs
# was missing, only that one of them was. Splitting on an observed boundary rather than on a
# reconstruction of the causes is what makes the two parts add up to the discard count exactly,
# with nothing left over.

# %%
features = built.select(["timestamp", "symbol", *feature_cols]).sort(["timestamp", "symbol"])
assert features.select(["timestamp", "symbol"]).is_duplicated().sum() == 0, "duplicate panel key"
incomplete = {c: features[c].null_count() for c in feature_cols if features[c].null_count()}
assert not incomplete, f"the gate left nulls behind: {incomplete}"
gaps = panel["premium_index_close"].is_null().sum()
first_complete = features.group_by("symbol").agg(pl.col("timestamp").min().alias("_first")).lazy()
discarded = (
    panel.lazy()
    .join(
        features.lazy().select("symbol", "timestamp").with_columns(pl.lit(True).alias("_kept")),
        on=["symbol", "timestamp"],
        how="left",
    )
    .filter(pl.col("_kept").is_null())
    .join(first_complete, on="symbol", how="left")
    .select((pl.col("timestamp") < pl.col("_first")).fill_null(True).alias("filling"))
    .collect()
)
filling_rows = int(discarded["filling"].sum())
print(f"{trailing.height:,} bars assembled, {features.height:,} complete on every feature")
print(f"{gaps:,} premium-index gaps in the input, {trailing.height - features.height:,} discarded")
print(f"  {filling_rows:,} of those are a contract still filling its windows after listing")
print(f"  {len(discarded) - filling_rows:,} are a missing input reaching through a window later")
assignment = assign_families(feature_cols, FAMILIES)
register_frame(FAMILIES, feature_cols).select(["family", "columns", "role", "representation"])

# %% [markdown]
# ### F1. Coverage through time
#
# Coverage is drawn on the panel the gate acts on rather than on the emitted matrix. On the emitted
# matrix it is a check that the policy ran - flat lines at exactly one, by construction, and nothing
# else to see. Drawn on what the gate reads, it shows where in the sample the coverage was lost.
#
# It does not, on its own, say why, and the dashed boundary is easy to over-read. That line is the
# earliest row the matrix emits - the settlement at which the *first* contracts to list finished
# filling their windows - and it says nothing about the rest. This panel is unbalanced, and every
# contract has its own warmup beginning on its own listing date, so almost every contract in the
# universe table above finishes filling somewhere to the right of that line, the ones listing in
# 2022 and 2023 by years. While any of them fills, the share of non-null rows across the panel
# falls. The dips through 2020 are that -
# contracts arriving and filling their windows, which the universe table above dates. The deeper
# dips from 2021 onward
# are premium-index gaps, which arrive at no particular time and hit the widest windows hardest.
# The count above separates the two over the whole sample; the figure shows when each happened.
# Both would shrink if the longest window were shortened, since a shorter window fills sooner and
# spans fewer gaps, but only the warmup is bounded by the window alone - it costs one stretch per
# contract and no more, while what the gaps cost also follows how many there are. The
# cross-sectional family is absent because it does not exist yet at this point: C.7 computes it
# after the gate, over the rows that survived.

# %%
plot_coverage_through_time(
    family_coverage(
        trailing, {c: f for c, f in assignment.items() if c in SYMBOL_COLS}, every="1mo"
    ),
    warmup_boundary=features["timestamp"].min(),
    title="Gaps in the premium index cost far more coverage than the warmup does",
    subtitle="Monthly non-null share per family before the null policy, on an axis scaled to the data",
    alt=(
        "Line chart of non-null share against date for the five per-symbol families - carry, mean "
        "reversion, momentum, volatility and regime - on a y-axis running from about 0.35 to one. "
        "Every family sits at one for most months, with sharp isolated dips scattered from 2020 "
        "to 2023 and a shallow one at the end of 2025. A dashed line at the left edge marks the "
        "first settlement at which the contracts listed at the start have filled their windows; "
        "the dips through the rest of 2020 are later contracts listing and filling theirs. The "
        "deepest dips come after that and are missing premium-index observations: mid-2021, where "
        "mean reversion falls to about 0.35 and volatility to about 0.6, then late 2022 and early "
        "2023. Mean reversion falls furthest at every dip because its longest window is the "
        "thirty-day percentile, and the other four follow it down by progressively less in the "
        "same months."
    ),
)

# %% [markdown]
# ### F4. The timing contract
#
# The register's two timing columns, drawn. Each bar runs leftward from the decision timestamp by
# that family's lookback, so its length is how far back the family reads. A family that waited for
# data - one whose newest input is published after the decision it feeds - would show a gap between
# the end of its bar and the decision line. None here does, because every observation any of these
# families reads is published no later than the decision timestamp itself. That is the condition
# that matters, and it is weaker than sharing a grid: the seven-day cash flow deliberately counts
# the shortened two- and four-hour settlements from Section B, which fall between the eight-hour
# decision times rather than on them, and those are knowable at the decision all the same.

# %%
plot_timing_contract(
    FAMILIES,
    bar_unit="settlement periods",
    title="Every family reads up to the settlement and none of them waits",
    subtitle="Register lookback per family; a gap at the right edge would be an information lag",
    alt=(
        "Horizontal bars, one per feature family, each extending leftward from the decision line "
        "by that family's lookback: ninety settlement periods for momentum and mean reversion, "
        "forty-three for carry and volatility, ten for regime and one for the cross-sectional "
        "family. Every bar reaches the decision line, and there is no hatched lag segment on any "
        "of them."
    ),
)

# %% [markdown] tags=["results"]
# The matrix carries **39 features** on **99,877 rows** across **19 perpetuals**, from
# **2020-01-31** to **2025-12-31**, under content digest **873623a4af13b3fc**. Assembly discarded
# **8,421** of the **108,298** settlement bars the panel starts with, and the **537** missing
# premium-index observations in the input account for most of that rather than the warmup does.

# %%
print(
    f"{len(feature_cols)} features, {len(features):,} rows, {features['symbol'].n_unique()} perps"
)
print(f"{features['timestamp'].min()} to {features['timestamp'].max()}")

# %% [markdown]
# ## F. What the features look like
#
# Four properties decide whether this matrix can be used at all: the scale each feature arrives on,
# whether the cross-section disagrees enough to rank on, how much of the set is one ordering under
# several names, and how long a value lasts. All four are descriptive, and none of them reads a
# label. Whether a feature predicts is a fold-aware question, and `05_evaluation` is where it is
# asked.
#
# ### F2. Feature distributions
#
# The percentile panel is a comb rather than the flat block a percentile usually draws, and that is
# the cross-section showing through: nineteen perpetuals admit at most nineteen distinct positions
# per settlement, and the panel is unbalanced, so the values it can take change with breadth. It is
# still comparable across dates, which is the property it was built for, but a model that expects a
# continuous input is being handed something closer to an ordered category.

# %%
plot_feature_distributions(
    features,
    [
        "funding_rate",
        "funding_rate_zscore_14d",
        "premium_level",
        "premium_zscore_14d",
        "premium_rank",
        "funding_half_life_14d",
    ],
    title="Normalizing spreads a spiked settled rate across a range a model can read",
    subtitle="The carry family, display tails clipped at the half-percent",
    alt=(
        "Six histograms in two rows. The raw funding rate and the premium level are both a narrow "
        "spike at zero with thin tails either side, and almost no usable spread. Their trailing "
        "z-scores are broad: the funding z-score peaks just above zero and trails off to the left "
        "to about minus four, the premium z-score is close to symmetric between minus three and "
        "three. The cross-sectional percentile is not smooth but a comb of isolated bars spread "
        "evenly across the range. The half-life is concentrated at the short end, with a tall bar "
        "at the lower clip and a body that thins out over the first few settlements."
    ),
)

# %% [markdown]
# ### F3. Cross-sectional dispersion through time
#
# A cross-sectional strategy needs the cross-section to disagree. On a settlement where the band
# narrows to nothing there is nothing to rank, whatever the average level of funding that day.

# %%
plot_cross_sectional_dispersion(
    features,
    "funding_rate",
    every="1mo",
    title="The gap between the most and least crowded perpetual shuts in quiet markets",
    subtitle="Monthly mean of the per-settlement 10th-90th percentile band of the funding rate",
    alt=(
        "Shaded band of the 10th to 90th percentile of the realized funding rate per settlement, "
        "averaged by month, with the median drawn through it. The band is widest through 2020 and "
        "2021, peaking sharply in the first quarter of 2021, then narrows to close to nothing "
        "from 2022 onward with only a brief reopening in early 2024. The median tracks the band "
        "and sits a little above zero for almost the whole sample."
    ),
)

# %% [markdown]
# ### F5. Redundancy structure
#
# Two features can be built from different quantities and still move together closely enough that
# a model has little to gain from carrying both. This screens for that. Every feature is ranked
# over the whole panel - all contracts, all settlements pooled - and the ranks are correlated, so
# the distance $1 - |\rho_s|$ is small for a pair that rises and falls together across the sample.
# The absolute value is what makes a feature and its negation land in the same group. The cut is
# drawn at the correlation the configuration calls redundant, and the merges to the right of it,
# at smaller distances, are the ones that exceed it.
#
# Two limits are worth carrying forward, because a dendrogram invites more confidence than this
# one has earned. A pooled correlation is not the cross-sectional ordering a long-short strategy
# acts on: two features can track each other over the sample and still rank the universe
# differently at a given settlement. And a correlation at the cut is a strong association, not
# collinearity - a linear model can still estimate both coefficients, less precisely. So this is
# an exploratory screen for what is worth investigating together, and picking one representative
# from each group is a fold-aware decision `05_evaluation` makes against the labels.

# %%
clusters = plot_redundancy_clusters(
    features,
    feature_cols,
    cut=REDUNDANCY_CUT,
    title="Adjacent horizons pair off; the premium and the settled rate stay apart",
    subtitle=r"Average linkage on $1 - |\rho_s|$, cut drawn at the redundancy threshold",
    alt=(
        "Dendrogram of all 39 features. The cut leaves 23 clusters, nine of which hold more than "
        "one feature. The largest is the normalized premium block, seven columns joined above the "
        "cut: both z-scores, all three percentile positions, and both deviations from a trailing "
        "mean. Two clusters hold three features each - the three premium volatility windows, and "
        "a cross-sectional group of the premium rank, the premium against the cross-sectional "
        "median, and the cross-sectional z-score. The other six are pairs: the realized funding "
        "rate with its seven-day cash flow; each oscillator with the premium change over its own "
        "window, once at one day and once at three; the regime indicator with premium "
        "persistence; the one-day premium volatility with the short volatility ratio; and the two "
        "price volatility windows. The remaining fourteen features stand alone and merge only "
        "near the root, among them the medium volatility ratio, the funding dispersion, the "
        "session marker and the premium level."
    ),
)

# %% [markdown]
# ### F6. Persistence and rank stability
#
# The autocorrelation on the left is of the feature, not of any return, so what it measures is how
# long a value lasts rather than how well it works. It is estimated per perpetual on pairs of
# settlements exactly one
# lag apart and summarized by the median over perpetuals, with a bootstrap interval: a correlation
# pooled over every symbol-settlement pair would read high whenever symbols sit at different
# levels, whether or not any one of them persists. The right-hand panel asks the same question of
# the ordering rather than the level, across consecutive rebalances - which here are consecutive
# settlements, because that is the cadence this case study trades at.
#
# Two readings are worth taking from it. The trailing volatility and the settled rate keep most of
# their ordering from one settlement to the next; the normalized premium features keep very little
# of theirs. That is a measurement of decay and nothing more - how fast a feature's value and its
# ordering change, with no label anywhere in it. It is the earliest warning of turnover a feature
# set can give: a ranking that is gone by the next rebalance would name a different set of
# positions each time it is read. Whether it does is not settled here, because what a strategy
# actually trades depends on how the ranking is mapped to positions, how many names are held, how
# they are weighted, and the minimum weight change and trade size the configuration sets before a
# rebalance happens at all. The backtest stages measure realized turnover under those rules; this
# figure says which features would drive it. Whether any of them predicts, at this horizon or a
# longer one, is a question `05_evaluation` asks against the labels, and this figure does not
# answer it in either direction.
#
# The second reading is that the oscillator turns negative at a lag equal to its own window, which
# is what a bounded average of a fixed number of differences does when the differences themselves
# carry no memory: it is measuring its own window rather than the market's.
#
# The right-hand panel needs the list of rebalance times to correlate one against the next. It
# indexes them through a Python dictionary, which carries microsecond precision, while this matrix
# is stamped to the millisecond, so the copy handed to the figure is cast to match. The emitted
# matrix keeps its own precision.

# %%
persistence_frame = features.with_columns(pl.col("timestamp").cast(pl.Datetime("us", "UTC")))
DECISION_DATES = persistence_frame["timestamp"].unique().sort().to_list()

plot_persistence(
    persistence_frame,
    ["funding_rate", "premium_zscore_14d", "premium_rank", "price_vol_14d", "premium_rsi_72h"],
    entity="symbol",
    max_lag=W["premium_zscore"]["14d"],
    decision_dates=DECISION_DATES,
    title="Volatility persists across rebalances; the normalized premium does not",
    subtitle="Median over perpetuals across two weeks of settlements; rank correlation across rebalances",
    alt=(
        "Two panels. On the left, autocorrelation against lag. The two-week price volatility "
        "starts at one and decays slowly to about 0.45 at the longest lag. The realized funding "
        "rate starts near 0.75 and falls to about 0.25. The premium z-score and the "
        "cross-sectional percentile both start near 0.25 and are at zero within about twenty "
        "settlements. The oscillator falls fastest, crossing zero and reaching about minus 0.35 "
        "at a lag equal to its own window before returning to zero. Bootstrap ribbons are narrow "
        "throughout. On the right, the rank correlation between consecutive rebalances orders "
        "them the same way: price volatility at one, the funding rate around 0.6, the percentile "
        "around 0.25, and the z-score and the oscillator both near 0.15."
    ),
)

# %% [markdown] tags=["results"]
# Read together, the four figures describe a matrix that is on usable scales, carries a lot of
# repetition, and turns over fast. The cross-section disagrees except in the quietest stretches,
# where there is little to rank; the **39** columns fall into **23** groups once features that
# move together over the sample are gathered; and only the trailing volatility and the raw settled
# rate keep their ordering from one settlement to the next, while the normalized premium features
# turn over almost completely. None of that is a statement about predictive content, which no
# figure here measures.

# %% [markdown]
# ## G. Emit
#
# The matrix is written to `features/financial.parquet`, and everything downstream reads it from
# there. [`04_model_based_features`](04_model_based_features.ipynb) opens the file directly, joins
# it to the primary label, and fits the volatility and regime features that sit on top of it, fold
# by fold. [`05_evaluation`](05_evaluation.ipynb) opens it directly too, and screens every column
# in it for information