Market Regime Detection

Notebook: notebooks/T_Finance_Regimes.ipynb

Abstract

Financial markets transition between distinct regimes — bull rallies, bear corrections, and crisis episodes — each exhibiting characteristic statistical properties. Traditional approaches rely on Hidden Markov Models or threshold rules applied to single indicators, losing the multi-dimensional structure of cross-sector dynamics.

ChronosVector (CVX) reframes regime detection as trajectory geometry in a high-dimensional feature space. We construct daily trajectories from 11 S&P 500 sector ETFs, each described by 7 features (close, volume, volatility, momentum, RSI, MACD, OBV), yielding a D=77 feature space. CVX’s PELT changepoint detection identifies 11 regime transitions, including the COVID-19 crash (severity=0.97) and the 2022 rate-hike correction. Rolling Hurst exponent analysis (H=0.744) confirms persistent trending behavior across market cycles. Depth-2 path signatures fingerprint each regime period, enabling signature-based regime classification with F1=0.704.

Regime Detection in Quantitative Finance

Hidden Markov Models (HMMs) are the dominant paradigm for market regime detection (Hamilton, 1989). A latent discrete state governs the observed returns, with transitions estimated via the Baum-Welch algorithm. While effective for univariate return series, HMMs struggle with high-dimensional feature spaces and impose restrictive distributional assumptions (typically Gaussian emissions).

Hurst Exponent and Long Memory. Lo (1991) introduced the rescaled range (R/S) analysis to finance, testing for long-range dependence in stock returns. A Hurst exponent H > 0.5 indicates persistent (trending) behavior; H < 0.5 indicates mean-reversion. Rolling Hurst estimation reveals how market memory structure changes across regimes — trending markets show H approaching 0.8, while choppy markets fall below 0.5.

Path Signatures for Financial Data. Lyons et al. pioneered the use of rough path theory and path signatures as feature maps for sequential data. In finance, Gyurko et al. (2013) and Arribas et al. (2020) demonstrated that truncated signatures capture essential geometric properties of price paths — direction, curvature, and cross-correlations — providing a principled alternative to hand-crafted technical indicators. Signatures are invariant to time reparametrization, making them robust to variations in trading activity.

CVX’s Contribution. Rather than fitting HMMs or computing signatures externally, CVX provides an integrated trajectory analytics stack: ingest multi-sector features as temporal points, detect changepoints natively, compute rolling Hurst exponents, and extract path signatures — all within a single graph-backed engine.

Methodology

Data Construction

Component	Detail
Assets	11 S&P 500 sector ETFs (XLK, XLF, XLV, XLE, XLI, XLY, XLP, XLU, XLB, XLRE, XLC)
Period	2018-01-01 to 2024-12-31 (~1,750 trading days)
Features per sector	Close, Volume, 20d Volatility, 20d Momentum, RSI-14, MACD, OBV
Total dimensionality	D = 11 sectors x 7 features = 77

CVX Pipeline

Ingestion: Daily 77-dimensional feature vectors ingested as TemporalPoint<f64, DateTime> into the CVX graph with HNSW indexing.
Anchor Projection: Three market regime anchors defined — bull (broad gains, low volatility), bear (broad losses, high volatility), crisis (extreme VIX, correlation spike). Each trading day projected onto anchor distances via drift().
Changepoint Detection: PELT algorithm (detect_changepoints) applied to the anchor-distance trajectory with minimum segment length of 20 trading days.
Hurst Exponent: Rolling hurst_exponent() with window=120 days characterizes memory structure within and across regimes.
Path Signatures: Depth-2 signatures (path_signature(depth=2)) computed per regime segment, yielding geometric fingerprints for classification.
Regime Prediction: Signature features fed to a logistic classifier for regime labeling (bull/bear/crisis).

CVX Functions Used

CVX Function	Purpose	Parameters
`cvx.ingest()`	Load daily 77-D vectors	`dim=77, metric="cosine"`
`cvx.drift()`	Anchor-relative trajectory	3 regime anchors
`cvx.detect_changepoints()`	PELT regime boundaries	`min_segment=20, penalty="bic"`
`cvx.hurst_exponent()`	Memory/persistence analysis	`window=120`
`cvx.path_signature()`	Geometric fingerprinting	`depth=2`
`cvx.velocity()`	Rate of regime transition	Per-segment
`cvx.trajectory()`	Full path extraction	Entity-level

Key Results

Changepoint Detection

PELT identifies 11 regime transitions across the 7-year analysis window:

#	Date	Event	Severity	Regime Transition
1	2018-10-10	Q4 2018 selloff	0.72	Bull to Bear
2	2019-01-04	Fed pivot recovery	0.61	Bear to Bull
3	2019-08-05	Trade war escalation	0.58	Bull to Correction
4	2019-10-11	Phase 1 deal optimism	0.53	Correction to Bull
5	2020-02-20	COVID-19 crash onset	0.97	Bull to Crisis
6	2020-03-23	Fed intervention bottom	0.89	Crisis to Recovery
7	2020-11-09	Vaccine rally	0.65	Recovery to Bull
8	2022-01-04	Rate hike selloff	0.81	Bull to Bear
9	2022-10-13	Bear market bottom	0.73	Bear to Recovery
10	2023-03-10	Banking crisis (SVB)	0.62	Recovery to Correction
11	2023-10-27	AI-driven rally	0.55	Correction to Bull

The COVID-19 transition (severity=0.97) represents the largest geometric displacement in the 77-dimensional feature space, consistent with the unprecedented cross-sector correlation spike.

Hurst Exponent Analysis

Regime	Mean Hurst	Interpretation
Bull (sustained)	0.78	Strongly persistent — trending
Bear (selloff)	0.71	Persistent — momentum continues
Crisis (COVID)	0.52	Near random walk — regime breakdown
Recovery	0.69	Moderate persistence
Overall	0.744	Persistent trending behavior

The drop to H=0.52 during the COVID crisis reflects the breakdown of cross-sector correlations and the loss of predictable trending behavior.

Regime Classification via Path Signatures

Depth-2 signatures yield 77 + 77^2/2 = 3,040 features per regime segment. After PCA reduction to 50 components:

Metric	Value
F1 (macro)	0.704
Precision	0.721
Recall	0.693
Accuracy	0.738

Signature-based classification outperforms HMM baselines (F1=0.63) on the same data, particularly for distinguishing correction from early-bear regimes.

Notebook Plots

The notebook produces the following interactive visualizations:

Regime Timeline: Stacked anchor-distance plot with changepoint markers and regime labels
Rolling Hurst Heatmap: Per-sector Hurst evolution across the full period
Signature PCA: 3D projection of regime signatures colored by label
Velocity Spikes: Transition velocity at each changepoint, sized by severity

Running the Notebook

# Install dependencies
pip install chronos-vector yfinance plotly scikit-learn

# Run analysis
cd notebooks && jupyter notebook T_Finance_Regimes.ipynb

Requirements: ~2 GB RAM, ~5 min for data download and CVX ingestion.