Quantitative Finance

Quantitative finance operates on high-dimensional, temporally structured data: factor returns evolve, correlations shift, and market regimes emerge and dissolve. ChronosVector (CVX) provides the temporal embedding infrastructure to reason about these dynamics natively.

Problem

Quant researchers need to:

• Match current market conditions to historical periods across hundreds of correlated features, accounting for both similarity and temporal proximity.
• Detect factor decay early by monitoring how factor embeddings drift over time, before traditional performance metrics reveal the degradation.
• Characterize market trajectory shapes — not just where the market is, but how it got there — for path-dependent pricing and strategy selection.

All of these require working in high-dimensional embedding spaces with first-class temporal semantics, which is exactly what CVX provides.

Data Model

Finance Concept	CVX Primitive
Market state	Vector (factor returns, correlations)
Trading day	Timestamp
Asset / strategy	Entity
Market regime	Region
Regime transition	Change point
Factor trajectory	Entity trajectory

A single market state vector might concatenate sector returns, cross-asset correlations, volatility surface features, and macro indicator embeddings. Each trading day produces a new observation, and CVX indexes them for both semantic and temporal retrieval.

Code Examples

Market Regime Matching via Temporal kNN

Find historical market states that resemble current conditions, weighted by both semantic similarity and temporal proximity:

# Find similar historical market states
results = index.search(vector=current_state, k=10, alpha=0.3, query_timestamp=today)
# alpha weighs temporal proximity vs semantic similarity

An alpha of 0.3 means the search is 70% driven by vector similarity and 30% by recency. Lower alpha values favor pure similarity regardless of when the state occurred; higher values prefer recent matches.

Factor Trajectory Analysis

Track how a factor embedding evolves and determine its statistical character:

traj = index.trajectory(entity_id=factor_id)
h = cvx.hurst_exponent(traj)
# H > 0.5: trending market → momentum strategies
# H < 0.5: mean-reverting → contrarian strategies

The Hurst exponent computed over the embedding trajectory reveals whether the factor is trending (H > 0.5), mean-reverting (H < 0.5), or following a random walk (H ≈ 0.5). This directly informs strategy selection.

Regime Transition Detection

Identify structural breaks in factor behavior:

changepoints = cvx.detect_changepoints(factor_id, traj)
# Each changepoint = potential regime shift

Change points mark moments where the underlying data-generating process shifts. In financial terms, these correspond to regime transitions — from low-vol to high-vol, from risk-on to risk-off, or from one correlation structure to another.

Velocity for Regime Transition Speed

Measure how fast the market is moving through embedding space:

vel = cvx.velocity(traj, timestamp=transition_ts)
# Velocity spikes indicate fast regime transitions

Velocity spikes at a detected change point indicate an abrupt regime shift (e.g., a flash crash or sudden policy change), while gradual velocity increases suggest a slow rotation.

Sector Rotation via Distributional Distances

Track how portfolio composition shifts across hierarchical market sectors:

reg_traj = index.region_trajectory(entity_id=portfolio_id, level=2)
wd = cvx.wasserstein_drift(dist_t1, dist_t2, centroids)
# Wasserstein respects sector distance: tech→fintech < tech→energy

The Wasserstein (earth mover’s) distance captures that rotating from technology into fintech is a smaller shift than rotating from technology into energy. This geometry-aware measure of distributional change is critical for understanding true portfolio drift.

Path Signatures for Trajectory Classification

Compute fixed-dimensional descriptors of market trajectories:

sig = cvx.path_signature(factor_traj, depth=2, time_augmentation=True)
# Fixed-dimensional descriptor invariant to reparametrization
# "Shape" of market move matters more than exact timing

Path signatures from rough path theory produce a canonical description of the trajectory shape. A V-shaped recovery and a slow grind-down have different signatures even if they start and end at the same point. Time augmentation preserves information about the speed of moves.

Portfolio Path Comparison

Compare how two portfolios moved through embedding space:

fd = cvx.frechet_distance(portfolio_traj_a, portfolio_traj_b)
sd = cvx.signature_distance(sig_a, sig_b)
# Signature distance O(K²) vs Fréchet O(nm)

Frechet distance measures the maximum deviation between two paths (the “dog-walking” distance), while signature distance compares their canonical shape descriptors. For long trajectories, signature distance is substantially more efficient.

Event Features for Trading Patterns

Characterize the temporal structure of trade arrival times:

ef = cvx.event_features(trade_timestamps)
# burstiness > 0: bursty trading → possible algorithmic activity
# memory > 0: trades cluster → herding behavior

Burstiness and memory coefficients reveal whether trading activity is uniform, bursty (algorithmic), or clustered (herding). These features complement volume analysis with temporal microstructure information.

Market Structure Topology

Analyze the topological features of sector-level embeddings:

topo = cvx.topological_features(sector_centroids)
# Fragmenting β₀ → market decoupling
# Converging β₀ → correlation spike (risk-off)

The zeroth Betti number (β₀) counts connected components in the sector embedding space. When β₀ increases, sectors are decoupling — correlations are breaking down and diversification is working. When β₀ drops toward 1, everything is converging — a classic risk-off correlation spike.

Example Workflow: Regime Detection Pipeline

A complete regime detection pipeline chains these primitives together:

1. Embed daily market states. Concatenate factor returns, rolling correlations, and macro indicators into a state vector and insert daily:

   index.bulk_insert(vectors=state_vectors, timestamps=trading_days, entity_ids=strategy_ids)

2. Query similar historical periods. Search for past states that resemble today, balancing similarity and recency:

   matches = index.search(vector=today_state, k=20, alpha=0.3, query_timestamp=today)

3. Retrieve forward trajectories. For each historical match, pull the trajectory of what happened next:

   forward_trajs = [index.trajectory(entity_id=m.entity_id) for m in matches]

4. Compute path signatures. Reduce each forward trajectory to a fixed-dimensional shape descriptor:

   sigs = [cvx.path_signature(t, depth=2, time_augmentation=True) for t in forward_trajs]

5. Classify dominant post-match pattern. Cluster signatures to identify the most common forward regime:

   # Compare signature distances to identify dominant pattern
   distances = [[cvx.signature_distance(a, b) for b in sigs] for a in sigs]

6. Inform position sizing. Use the dominant forward pattern and its frequency to calibrate conviction and position size.

This pipeline answers the question: “Given that the market looks like this today, what usually happened next, and how confident should we be?”

References

• Lopez de Prado, M. — Information-driven sampling methods for financial machine learning, including triple-barrier labeling and entropy-based feature selection for non-stationary financial data.
• Hamilton, J. D., Waggoner, D. F., & Zha, T. (2016) — Regime-switching models for identifying structural breaks in financial time series and macroeconomic data.