Kinematic Finance Portal

Topological Data Analysis finds patterns in the market's geometry. Our API computes persistent homology in real-time—you get early warning signals before price confirms.

Topological Data Analysis

TDA is a mathematical framework for analyzing the "shape" of data. Rather than looking at individual price points, we examine the overall structure and persistent features of the data cloud.

Key Concepts

Persistent Homology

We track topological features (loops, voids, connected components) as we vary a scale parameter. Features that persist across multiple scales are considered significant.

Betti Numbers

**β₀**: Number of connected components (market regimes)

**β₁**: Number of loops (consolidation patterns)

**β₂**: Number of voids (complex structures)

The TDA Precursor

Our research shows that changes in topological features often precede significant market moves. Specifically:

1. **Loop Formation**: During consolidation, a loop forms in state space

2. **Loop Persistence**: The loop grows and stabilizes

3. **Loop Death**: When the loop disappears, a breakout occurs

Why It Works

Topological features are:

**Robust to noise**: Small price fluctuations don't affect the overall shape

**Scale-independent**: Work across different timeframes

**Predictive**: Changes in topology precede changes in price

Signal Generation

We monitor:

Loop birth and death events

Changes in Betti numbers

Wasserstein distances between persistence diagrams

These topological changes generate our trading signals.

Access API/MCP/X402 View Terminal