Kinematic Finance
Back to concepts
Topological Analysis

TDA Precursor Visualizer

Topological data analysis for identifying persistent market structures

Loading visualization...
Interactive - Touch/mouse to explore
Share:

Key Features

  • Persistent homology computation
  • Betti number tracking
  • Loop birth/death events
  • Topological feature persistence
  • Multi-scale analysis

Technical Specs

Algorithm
Persistent homology (Vietoris-Rips)
Dimensions
H₀, H₁, H₂ homology groups
Filtration
Multi-scale epsilon values
Computation
Optimized simplicial complex
Output
Persistence diagrams and barcodes

Use Cases

  • 1
    Market regime detection
  • 2
    Crisis prediction
  • 3
    Structural break identification
  • 4
    Pattern persistence analysis
  • 5
    Risk management applications

Documentation


Topological Data Analysis

TDA reveals the shape and structure of financial data by analyzing topological features that persist across multiple scales. This approach uncovers hidden patterns in market behavior.


Core Concepts

Persistent Homology

  • **H₀**: Connected components (market regimes)
  • **H₁**: Loops (consolidation patterns)
  • **H₂**: Voids (complex market structures)

    • Filtration Process

  • Start with discrete data points
  • Gradually connect nearby points
  • Track topological feature birth/death
  • Identify persistent structures

    • Visualization Components

    Persistence Diagrams

  • Birth vs death times of features
  • Diagonal represents noise
  • Distance from diagonal = persistence
  • Color coding by feature type

    • Barcode Plots

  • Horizontal bars show feature lifespans
  • Length indicates persistence
  • Stacked by homology dimension
  • Interactive filtering

    • Point Cloud Evolution

  • 3D visualization of data points
  • Dynamic connection formation
  • Feature highlighting
  • Scale parameter control

    • Signal Generation

    Loop Events

  • **Birth**: New consolidation pattern
  • **Death**: Breakout signal
  • **Persistence**: Pattern strength
  • **Multiplicity**: Pattern complexity

    • Regime Detection

  • Connected component analysis
  • Cluster stability measurement
  • Transition point identification
  • Confidence intervals

    • Applications

    Risk Management

  • Early warning systems
  • Stress testing
  • Portfolio diversification
  • Tail risk assessment

    • Trading Applications

  • Breakout prediction
  • Consolidation identification
  • Trend confirmation
  • Market timing