Correlation Regime

Correlation-Regime Detection and Crisis Attribution

Overview

The correlation-analysis skill answers "how correlated are these assets?" — a snapshot. This skill answers the temporal questions a snapshot cannot:

1. When did the market fuse into one highly-correlated bloc, and when did it release? (Mode 1 — regime detection)
2. What does a fused regime mean for position sizing? (Mode 2 — risk context)
3. Who moved first when a crisis broke — is there a nameable trigger asset? (Mode 3 — first-mover attribution)
4. Who quietly rewired their relationship to the rest of the market, even without a violent move? (Mode 4 — rewiring leaderboard)

The methodology comes from an open-source streaming pipeline (see References) whose public repository pins the regime machinery's math and an eight-event historical replay regression (COVID, May-2021, China ban, Nov-2021 top, LUNA, FTX, SVB, yen-carry — 17 crypto symbols, 1-minute bars) that its CI reproduces bit-for-bit. The finer-grained numbers quoted in this skill — 13 fused/defused regime cycles on the continuous 2020–2024 tape at a ~0.008/day calm false-alarm rate, and zero wrong culprit names across 10 labeled crises (2 held out-of-sample), including naming FTT roughly two days before the November 2022 collapse — are the author's unpublished internal replays on that same pipeline and are not independently verifiable. All of it is historical replay, never live results, and the method is market-agnostic even though the validation tape is crypto.

What this skill is NOT: a trade-timing signal. The same validation program tested regime-based exits head-to-head against a plain price stop and lost — correlation regimes cannot time tops, and the give-up cost of selling into a crash is a property of the tape, not of any signal. Use these modes for risk context, monitoring, and post-hoc attribution; never present them as buy/sell triggers.

Mode 1: Correlation-Regime Detection (Edge Density + Hysteresis)

Use case: Maintain a live, causal answer to "is the market currently one bloc?" Diversification quietly disappears when pairwise correlations fuse; a regime state machine turns that into an explicit, monitorable state with few false alarms.

Workflow

1. Compute rolling-window pairwise correlations of returns
2. Reduce each correlation matrix to one number: edge density
   = fraction of asset pairs with |ρ| ≥ edge_threshold
3. Smooth the density series with a TRAILING window (causal — see warning below)
4. Run a hysteresis (Schmitt-trigger) state machine over the smoothed series:
   enter FUSED when density ≥ enter_threshold, exit only when ≤ exit_threshold
5. Emit regime state + transition timestamps for monitoring / reporting

Two thresholds with a dead band between them are the entire trick: a single threshold chatters (fires dozens of times as density oscillates around it), while hysteresis yields a handful of clean regime cycles per market cycle.

import numpy as np
import pandas as pd


def compute_edge_density(
    returns: pd.DataFrame,
    corr_window: int = 60,
    edge_threshold: float = 0.5,
) -> pd.Series:
    """Reduce rolling correlation matrices to an edge-density series.

    Edge density is the fraction of distinct asset pairs whose rolling
    |correlation| clears ``edge_threshold`` — a scalar "how fused is the
    market" gauge in [0, 1].

    Args:
        returns: Multi-asset return matrix, columns are symbols
        corr_window: Rolling window length (bars) for pairwise correlation
        edge_threshold: |ρ| level at which a pair counts as an "edge"

    Returns:
        Edge-density series aligned to ``returns.index`` (NaN during warmup)
    """
    n_assets = returns.shape[1]
    n_pairs = n_assets * (n_assets - 1) // 2
    upper_mask = np.triu(np.ones((n_assets, n_assets), dtype=bool), k=1)

    density = pd.Series(np.nan, index=returns.index)
    for i in range(corr_window, len(returns) + 1):
        corr = returns.iloc[i - corr_window:i].corr().abs().to_numpy()
        density.iloc[i - 1] = float((corr[upper_mask] >= edge_threshold).sum()) / n_pairs
    return density


def detect_regimes(
    density: pd.Series,
    smooth_window: int = 5,
    enter_threshold: float = 0.65,
    exit_threshold: float = 0.45,
) -> pd.DataFrame:
    """Hysteresis (Schmitt-trigger) regime state machine on smoothed density.

    The market is FUSED once smoothed density reaches ``enter_threshold`` and
    stays FUSED until it falls back to ``exit_threshold``. The dead band
    between the two thresholds is what suppresses chatter.

    Args:
        density: Edge-density series from :func:`compute_edge_density`
        smooth_window: Trailing smoothing window (causal; never centered)
        enter_threshold: Density level that opens a FUSED regime
        exit_threshold: Density level that closes it (must be < enter_threshold)

    Returns:
        DataFrame with columns ``density``, ``smoothed``, ``fused`` (0/1)
    """
    if exit_threshold >= enter_threshold:
        raise ValueError("exit_threshold must be below enter_threshold")

    # Trailing mean = causal. A centered window here silently reads the future.
    smoothed = density.rolling(smooth_window, min_periods=1).mean()

    fused = False
    states = np.zeros(len(smoothed), dtype=int)
    for i, value in enumerate(smoothed.to_numpy()):
        if np.isnan(value):
            states[i] = int(fused)
            continue
        if not fused and value >= enter_threshold:
            fused = True
        elif fused and value <= exit_threshold:
            fused = False
        states[i] = int(fused)

    return pd.DataFrame(
        {"density": density, "smoothed": smoothed, "fused": states},
        index=density.index,
    )

Threshold Selection Guide

Look-Ahead Warning

The single most common silent bug in regime detection is centered smoothing (e.g. rolling(..., center=True) or any symmetric filter). It leaks up to half a window of future data into each point, making historical regime onsets appear earlier and cleaner than anything achievable live. Every smoothing step in a regime pipeline must be trailing-only, and any claimed onset lead time should be re-checked after replacing each filter with its causal version — in the author's internal replays that re-check moved onsets later by 1–2 days and the detector still passed, which is the honest number to quote.

Mode 2: Regime-Aware Risk Context (De-Grossing)

Use case: Translate the FUSED state into portfolio-risk language for a report or a monitoring dashboard.

A fused regime means cross-asset diversification is effectively gone: the portfolio has collapsed into a single position with leverage. The defensible, replay-tested framing for what to do about it:

• De-gross, don't liquidate. In the author's internal replays, halving gross exposure during fused regimes improved risk-adjusted outcomes versus buy-and-hold, while going fully to cash destroyed them — regime onset lags the price top, so full liquidation locks in the worst prints.
• State the anti-claim in the same breath: fused-regime detection cannot time tops. Tested against a plain trailing price stop, regime-based exits lost; the ~double-digit "give-up" between a crash's start and any regime confirmation is a property of crash tapes themselves.

def regime_exposure_context(
    regimes: pd.DataFrame,
    base_gross: float = 1.0,
    fused_gross: float = 0.5,
) -> pd.Series:
    """Descriptive gross-exposure context per bar (NOT a trade signal).

    Args:
        regimes: Output of :func:`detect_regimes`
        base_gross: Reference gross exposure during defused (calm) regimes
        fused_gross: Reference gross exposure during fused regimes

    Returns:
        Per-bar reference gross-exposure series for risk reporting
    """
    return pd.Series(
        np.where(regimes["fused"] == 1, fused_gross, base_gross),
        index=regimes.index,
        name="reference_gross",
    )

Mode 3: Crisis First-Mover Attribution

Use case: A crisis episode has opened (Mode 1 fired, or an exogenous alert arrived). Answer "who broke first?" without ever guessing.

The Honesty Protocol

The protocol's defining property is that it prefers silence to a wrong name. Every episode resolves to exactly one of four verdicts:

In the author's internal 10-crisis replays (unpublished — see Overview) this protocol never emitted a wrong NAME — because the alarm bar is set very high and everything below it downgrades to AMBIGUOUS, MACRO, or ABSTAIN.

Workflow

1. For each asset, compute a short-horizon move-intensity series
   (rolling sum of |returns|)
2. Score it as a robust z-score against the asset's OWN calm baseline
   (median/MAD, baseline strictly prior to the bar being scored)
3. Watch tier (low z): informational watchlist only — never allowed to accuse
4. Alarm tier (very high z): record each asset's first crossing time
5. Apply the verdict rules: lead-gap ⇒ NAME, pack-together ⇒ MACRO,
   near-tie leaders ⇒ AMBIGUOUS, no crossings ⇒ ABSTAIN

def first_mover_attribution(
    returns: pd.DataFrame,
    baseline_window: int = 120,
    move_window: int = 3,
    alarm_z: float = 8.0,
    watch_z: float = 3.0,
    lead_gap: int = 2,
    macro_span: int = 1,
    macro_fraction: float = 0.6,
) -> dict:
    """First-mover crisis attribution with abstention.

    Each asset's short-horizon move intensity is scored as a robust z-score
    against its own trailing calm baseline (median / MAD, shifted so the move
    being scored never contaminates its own baseline). Verdicts follow the
    honesty protocol: NAME only on a clear solo lead, otherwise MACRO /
    AMBIGUOUS / ABSTAIN.

    Args:
        returns: Multi-asset return matrix, columns are symbols
        baseline_window: Trailing window (bars) for the per-asset calm baseline
        move_window: Short horizon (bars) of the move-intensity sum
        alarm_z: Robust z at which an asset counts as "in violent collapse"
        watch_z: Informational watch-tier level (never used for naming)
        lead_gap: Minimum lead (bars) of the first crosser over the second
            required to NAME it
        macro_span: If the pack crosses within this many bars of the first
            crossing, the episode is MACRO
        macro_fraction: Fraction of assets that must cross to call MACRO

    Returns:
        Dict with ``verdict`` (NAME / MACRO / AMBIGUOUS / ABSTAIN),
        ``named`` (symbol or None), ``candidates``, ``crossings``
        (symbol → first alarm timestamp), ``watchlist``, and ``z`` (the
        full z-score DataFrame for inspection)
    """
    intensity = returns.abs().rolling(move_window).sum()
    # Proper rolling MAD: each window's deviations from its OWN median.
    # (Nesting two full-length rolling medians instead stacks their warmups —
    # the score would silently stay NaN for 2x baseline_window bars.)
    # shift(1) keeps the bar being scored out of its own baseline.
    med = intensity.rolling(baseline_window).median().shift(1)
    mad = intensity.rolling(baseline_window).apply(
        lambda window: np.median(np.abs(window - np.median(window))), raw=True
    ).shift(1)
    z = (intensity - med) / (1.4826 * mad.replace(0.0, np.nan))

    crossings: dict[str, pd.Timestamp] = {}
    for symbol in z.columns:
        hits = z.index[z[symbol] >= alarm_z]
        if len(hits) > 0:
            crossings[symbol] = hits[0]

    watch_hits = (z >= watch_z).any()
    watchlist = sorted(watch_hits.index[watch_hits])

    if not crossings:
        return {
            "verdict": "ABSTAIN", "named": None, "candidates": [],
            "crossings": {}, "watchlist": watchlist, "z": z,
        }

    ordered = sorted(crossings.items(), key=lambda item: item[1])
    first_symbol, first_time = ordered[0]
    positions = {ts: i for i, ts in enumerate(z.index)}
    first_pos = positions[first_time]

    pack_size = sum(
        1 for _, ts in ordered if positions[ts] - first_pos <= macro_span
    )
    if pack_size >= max(2, int(np.ceil(macro_fraction * returns.shape[1]))):
        return {
            "verdict": "MACRO", "named": None,
            "candidates": [s for s, _ in ordered],
            "crossings": crossings, "watchlist": watchlist, "z": z,
        }

    leaders = [
        symbol for symbol, ts in ordered if positions[ts] - first_pos < lead_gap
    ]
    if len(leaders) == 1 and (
        len(ordered) == 1 or positions[ordered[1][1]] - first_pos >= lead_gap
    ):
        return {
            "verdict": "NAME", "named": first_symbol, "candidates": leaders,
            "crossings": crossings, "watchlist": watchlist, "z": z,
        }

    return {
        "verdict": "AMBIGUOUS", "named": None, "candidates": leaders,
        "crossings": crossings, "watchlist": watchlist, "z": z,
    }

Calibration Discipline

• The alarm bar must be chosen walk-forward on historical events whose culprit labels come from the public record (post-mortems, filings) — never from the system's own output. "The culprit is whoever we named" is circular and voids any zero-false-names claim.
• Baseline from detected calm, not from a blind trailing window, in production: source the median/MAD baseline from Mode 1's defused regimes. Trailing windows that overlap a previous crisis produce contaminated baselines and inflated bars — this was a real failure class in validation (post-crisis "calm" that wasn't).
• Set the bar high and let the protocol abstain. A bar low enough to catch every event mislabels non-events; the validated posture is "when it names, it has been right; when it cannot know, it says so."

Mode 4: Correlation-Rewiring Leaderboard

Use case: Catch the slow bleed-outs. Some collapses (weeks-long, grinding) never move violently enough to trip Mode 3's alarm — but the dying asset's correlation profile to the rest of the market rewires dramatically. Rank assets by how much their correlation row changed versus calm.

Modes 3 and 4 cover each other's blind spots — fast violent collapses trip the alarm, slow bleeds top the rewiring board — so report them together, never alone.

Choose the event window with care: during a full-market fusion episode every asset rewires by construction and the leaderboard degenerates into "everyone". The mode is most informative on the run-up window before a regime onset, or on a suspect stretch that never fused at all (the classic slow-bleed shape).

def rewiring_leaderboard(
    returns: pd.DataFrame,
    calm_mask: pd.Series,
    event_mask: pd.Series,
    min_bars: int = 40,
) -> pd.DataFrame:
    """Per-asset correlation-rewiring score: event vs calm baseline.

    Score = row mean of |Δρ| between the event-window correlation matrix and
    the calm-baseline correlation matrix. High score = the asset's
    relationship to the rest of the market changed the most.

    Args:
        returns: Multi-asset return matrix, columns are symbols
        calm_mask: Boolean series marking calm-baseline bars
            (e.g. ``regimes["fused"] == 0`` from Mode 1)
        event_mask: Boolean series marking the episode under examination
        min_bars: Minimum bars required in each window

    Returns:
        DataFrame indexed by symbol with ``rewiring_score``, sorted descending
    """
    calm = returns.loc[calm_mask.reindex(returns.index, fill_value=False)]
    event = returns.loc[event_mask.reindex(returns.index, fill_value=False)]
    if len(calm) < min_bars or len(event) < min_bars:
        raise ValueError(
            f"need >= {min_bars} bars in each window "
            f"(calm={len(calm)}, event={len(event)})"
        )

    delta = (event.corr() - calm.corr()).abs()
    matrix = delta.to_numpy(copy=True)  # copy: DataFrame internals may be read-only
    np.fill_diagonal(matrix, np.nan)
    scores = pd.Series(np.nanmean(matrix, axis=1), index=delta.index)
    return scores.sort_values(ascending=False).to_frame("rewiring_score")

Dependencies

pip install pandas numpy

(matplotlib only if you plot the regime timeline.)

Output Format

## Correlation-Regime and Attribution Report

### Universe: [N assets] ([Start Date] - [End Date], [bar size])

#### Regime Summary (Mode 1)
| Metric | Value |
|------|-----|
| Regime cycles (fused/defused) | 5 |
| Time in fused regime | 18% |
| Current state | DEFUSED (density 0.31, smoothed 0.34) |
| Last transition | 2024-08-05 fused → 2024-08-19 defused |

#### Risk Context (Mode 2)
| Regime | Reference gross | Rationale |
|------|-----|------|
| Defused | 1.00 | Diversification intact |
| Fused | 0.50 | Portfolio ≈ one levered position; de-gross, don't liquidate |

> Not a trade signal: regime detection cannot time tops (validated).

#### Episode Attribution (Mode 3)
| Field | Value |
|------|-----|
| Verdict | NAME |
| Named asset | [SYMBOL] (alarm z = 9.4, lead 2 bars over the pack) |
| Watchlist (informational) | [SYM1], [SYM2] |

#### Rewiring Leaderboard (Mode 4)
| Rank | Asset | Rewiring score |
|------|------|------|
| 1 | [SYMBOL] | 0.42 |
| 2 | [SYMBOL] | 0.19 |

Notes

1. Causality is the whole game. No centered smoothing, no same-bar baselines, no thresholds tuned on the episode being scored. Every historical claim should survive the question "could this have been computed at that bar?"
2. Not a trading signal. Regime exits were tested against a plain price stop and lost. Present Modes 1–4 as risk context and attribution, never as buy/sell.
3. Thresholds do not port across correlation estimators. An edge_threshold calibrated on raw-return correlations is wrong for partial/residual correlations (their edges are systematically smaller). Recalibrate per estimator.
4. Event-window scans are left-censored. Markets often re-fuse faster than a short scan can see; prefer one continuous tape over stitched event windows when validating regime counts.
5. Survivor bias truncates attribution. Delisted assets vanish from vendor tapes precisely when they matter most (the dying asset is the story). Pull raw histories that include delisted symbols before validating Mode 3/4 claims.
6. Scope of the attribution claim. The alarm mechanically names only fast, violent collapses; slow bleeds surface in the watch tier and Mode 4; macro shocks resolve to MACRO by construction. Quote the calm-period false-alarm rate (per day) as the honesty metric.
7. Labels are human, walk-forward. Culprit labels for calibration events come from the public record before scoring runs, and future re-calibration uses only events fully adjudicated in the past.
8. MAD can be zero in dead markets (stale prints); guard the denominator (the snippet maps 0 → NaN) rather than letting z-scores explode.

References

• Streaming reference implementation (JVM): the corrcalc-graphs pipeline — https://github.com/tarvyn-analytics/corrcalc-graphs-pipeline (Apache-2.0). Its README's "The math — from bars to a fire" section derives the density/hysteresis regime machinery, and "Validation — a pinned historical-event regression" pins an eight-event crypto replay regression (17 symbols, 1-minute bars) reproduced by its CI. The finer-grained numbers quoted in this skill (regime-cycle count, false-alarm rate, attribution results) are the author's unpublished internal replays on that pipeline — they are not part of the public regression and the public repo ships no crisis-naming system.
• Maven Central artifacts for JVM users: io.github.tarvyn-analytics.corrcalc:corrcalc-lib-core (streaming correlation engine), io.github.tarvyn-analytics.graphs:graphs-algos-lib (graph analyses on correlation matrices), io.github.tarvyn-analytics.corrcalc.graphs:corrcalc-graphs-pipeline (the replay pipeline).
• For static pair analysis, cointegration, and pair-trading signals, see the correlation-analysis skill; for volatility-based regime work, see volatility.