# FracJax 🚀

**High-Performance Fractal & Econophysics Tools for Financial Time Series using JAX.**

[![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](https://opensource.org/licenses/MIT)
[![Python](https://img.shields.io/badge/python-3.9+-blue.svg)](https://www.python.org/downloads/)
[![JAX](https://img.shields.io/badge/backend-JAX-green.svg)](https://github.com/google/jax)

FracJax is a production-grade Python library designed for quantitative finance and econophysics. It leverages **Google JAX** to perform heavy fractal and multifractal analysis on financial time series with **GPU acceleration**, achieving speeds up to **300x faster** than standard CPU-based libraries (like `nolds` or `hurst`).

> **Key Feature:** FracJax combines modern statistical robustness (Theil-Sen Estimator) with fractal theory (DFA, Wavelet Leaders) to extract noise-free, lag-free market regime signals.

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## ⚡ Why FracJax?

| Feature | Standard Libs (`nolds`/`hurst`) | FracJax |
| :--- | :--- | :--- |
| **Backend** | CPU (NumPy) | **GPU/TPU (JAX)** |
| **Speed (1M points)** | ~5-10 Minutes | **~1 Second** |
| **Regression** | Least Squares (Sensitive to noise) | **Theil-Sen (Robust to outliers)** |
| **Microscope** | Monofractal only | **Multifractal (Wavelet Leaders)** |
| **Stability** | Fails on short windows (<100) | **Stable on short windows** |

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## 📦 Features

FracJax calculates 10+ advanced market features across multiple dimensions:

### 1. Fractal & Memory (The "Market Microscope")
* **DFA (Detrended Fluctuation Analysis):** Robust long-term memory estimation (Trend vs. Mean Reversion).
* **Wavelet Leaders:** Multifractal singularity spectrum analysis (Detects structural shocks).
* **Higuchi Fractal Dimension:** Measures market roughness and complexity.

### 2. Microstructure & Liquidity
* **Rolling CVD Proxy:** Estimates aggressive buy/sell pressure from OHLCV.
* **Amihud Illiquidity:** Measures price impact per unit of volume.

### 3. Volatility & Risk
* **GARCH(1,1) Forecast:** Forward-looking volatility prediction.
* **Realized Semivariance (RSV):** Downside-specific volatility measure.
* **Hill Estimator:** Tail risk and fat-tail index estimation.

### 4. Information Theory & Inter-market
* **Permutation Entropy:** Measures time-series chaos and unpredictability.
* **Cointegration Z-Score:** Robust spread analysis between asset pairs.
* **Lead-Lag Mutual Information:** Measures non-linear information flow between assets (using Gaussian KDE).

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## 🛠 Installation


```bash

pip install fracjax .
```
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### 🚀 Quick Start
FracJax provides a high-level API create_market_microscope that JIT-compiles kernels for maximum speed.

```Python

import numpy as np
from fracjax import create_market_microscope

# Generate dummy price data (Random Walk)
prices = np.cumsum(np.random.randn(10000)) + 1000

# 1. Initialize Kernels (Compiles once)
# Method options: 'dfa', 'wavelet', 'higuchi', 'garch', 'cvd', etc.
calc_dfa = create_market_microscope(
    method='dfa', 
    window_size=100, 
    batch_size=4096
)

calc_wavelet = create_market_microscope(
    method='wavelet', 
    window_size=100,
    max_level=4
)

# 2. Run on Data (Ultra Fast)
hurst_dfa = calc_dfa(prices)
hurst_wavelet = calc_wavelet(prices)

print(f"DFA Signal (Last): {hurst_dfa[-1]:.4f}")
```
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### 📊 Visual Showcase
FracJax reveals the hidden anatomy of the market. Below is a dashboard generated using FracJax on 7 years of Forex data (60-day zoom):

(Note: Replace this link with your actual image path after uploading)

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### 🤝 Contributing
Contributions are welcome! Please ensure any PRs maintain JAX functional purity (no side effects) and include type hints.

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### 📄 License
This project is licensed under the MIT License - see the LICENSE file for details.

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