mbvlgranger 0.1.0

Multi-Band Variable-Lag Granger Causality: A Unified Framework for Causal Time Series Inference across Frequencies

MBVL-Granger: MultiBand Variable-Lag Granger Causality Analysis

A Python framework to infer causality between time series using MultiBand Variable-Lag Granger causality with frequency-band decomposition.

Traditional Granger causality assumes fixed time delays between cause and effect. However, for non-stationary time series, this assumption often fails. For example, in neural signals, the delay between brain regions can vary over time due to changing network dynamics.

We propose MBVL-Granger that allows variable-lags and analyzes causality within specific frequency bands to handle complex, non-stationary time series relationships.

Installation

You can install our package from PyPI:

pip install mbvlgranger

For the newest version from GitHub:

git clone https://github.com/Teddy50060/mbvlgranger.git
cd mbvlgranger
pip install -e .

Example: Gas Furnace Data Analysis

First, we load time series data where gas input rate (X) potentially causes CO2 concentration (Y) with variable delays.

import numpy as np
import scipy.io
from mbvlgranger import quick_mbvlgranger

# Load gas furnace data
mat_data = scipy.io.loadmat('data/gasfurnace.mat')
x = np.array(mat_data['gasfurnace'][0]).flatten()  # Gas input rate
y = np.array(mat_data['gasfurnace'][1]).flatten()  # CO2 concentration

We use the following function to infer whether X causes Y across different frequency bands:

# Run MBVL-Granger analysis
results = quick_mbvlgranger(
    x=x, y=y,
    fs=250,  # sampling frequency
    max_lag=50,
    bands={
        'slow': (1, 10),       # Slow thermal dynamics
        'medium': (11, 25),    # Medium process dynamics
        'fast': (26, 50),      # Fast control responses
        'rapid': (51, 100)     # Rapid fluctuations
    }
)

The result of MBVL-Granger causality analysis:

print(f"Overall Causality: {results['overall_causality']}")
print(f"Combined p-value: {results['combined_p_value']:.6f}")

# Actual output:
# Overall Causality: True
# Combined p-value: 0.000000

If results['overall_causality'] is True, then X MBVL-Granger-causes Y. The combined_p_value indicates statistical significance across all frequency bands.

For individual frequency band results:

from mbvlgranger import print_mbvlgranger_results

# Print detailed results for each frequency band
print_mbvlgranger_results(results)

# Actual output:
# VL-Granger Frequency Causality Analysis Results
# ==================================================
# Overall Causality: True
# Combined P-value: 0.000000
# Method: fisher
# Valid Bands: 4
# 
# Individual Band Results:
# --------------------------------------------------
# 1-10Hz   | F=32.014 | p=0.000000 | BIC= 0.746 | Lag= 3 | Sig=YES
# 11-25Hz  | F= 0.000 | p=1.000000 | BIC=-27.633 | Lag= 4 | Sig=NO
# 26-50Hz  | F= 0.996 | p=0.492149 | BIC= -1.279 | Lag= 4 | Sig=NO
# 51-100Hz | F= 0.663 | p=0.952331 | BIC= -1.492 | Lag=12 | Sig=NO

Core Analysis

For more control over the analysis:

from mbvlgranger import VLGrangerCausality

# Single time series analysis with core algorithm
analyzer = VLGrangerCausality()
result = analyzer.analyze_causality(Y=y, X=x, max_lag=25, gamma=0.5)

print(f"Causality detected: {result['XgCsY']}")
print(f"Detected lag: {result['following_result']['opt_delay']}")
print(f"BIC ratio: {result['BIC_diff_ratio']:.3f}")

Citation

If you use MBVL-Granger in your research, please cite:

@article{mbvlgranger2024,
    title={MultiBand Variable-Lag Granger Causality Analysis},
    author={Your Name},
    journal={Journal Name},
    year={2024}
}