Tutorials and Examples

The timecorr package provides comprehensive tutorials to help you get started with dynamic correlation analysis. These tutorials cover everything from basic concepts to advanced applications across multiple domains.

Getting Started

If you’re new to timecorr, we recommend starting with the synthetic data tutorial to understand the core concepts and functionality.

Core Tutorials

Fundamental Concepts

• Synthetic Data Tutorial: Exploring Dynamic Correlations
  • Introduction
  • 1. Synthetic Data Generation
  • 2. Visualizing Synthetic Data
  • 3. Kernel Functions for Dynamic Correlations
  • 4. Computing Dynamic Correlations
  • 5. Visualizing Dynamic Correlations
  • 6. Higher-Order Correlations
  • 7. Multi-Subject Analysis
  • 8. Statistical Analysis and Significance Testing
  • 9. Summary and Best Practices
• Applications Tutorial: Dynamic Correlations Across Research Domains
  • Introduction
  • 1. Neuroscience Application: Brain Network Connectivity
  • 2. Economic Application: Market Correlation Analysis
  • 3. Climate Science Application: Environmental Variable Relationships
  • 4. Social Sciences Application: Social Network Dynamics
  • 5. Summary and Best Practices for Different Domains
• Using timecorr
• Using timecorr: A Comprehensive Guide
  • Key Concepts
  • Applications
• Load in required libraries
• Simulate some data
• Data Simulation
  • Simulation Parameters
• Understanding Vectorized vs. Matrix Format
  • Format Conversion
• Higher order correlations
• Higher-Order Correlations: Preventing Dimension Explosion
  • The Problem
  • The Solution: Dimensionality Reduction (rfun)
• Summary and Next Steps
  • What We’ve Covered
  • Key Parameters Summary
  • Real-World Applications
  • Advanced Topics
  • Next Steps

Synthetic Data Tutorial

Learn the fundamentals of timecorr using synthetic datasets:

• Generate different types of synthetic data (random, block, ramping, constant)

• Explore various kernel functions and their effects on correlation estimates

• Understand dynamic correlations and higher-order correlation analysis

• Perform multi-subject analysis with ISFC and WISFC methods

• Conduct statistical testing and significance assessment

Location: docs/tutorial/synthetic_data_tutorial.ipynb

Applications Tutorial

Discover real-world applications across multiple research domains:

• Neuroscience: Brain network dynamics and functional connectivity patterns

• Economics: Market correlations and financial network analysis

• Climate Science: Environmental variable relationships over time

• Social Sciences: Social network dynamics and behavioral pattern analysis

Location: docs/tutorial/applications_tutorial.ipynb

Key Concepts Covered

Weighting Functions

• Gaussian weights: Smooth temporal averaging with adjustable variance

• Laplace weights: Sparser temporal kernels for precise timing

• Mexican Hat weights: Derivative-based kernels for temporal dynamics

• Custom kernels: How to define your own weighting functions

Correlation Methods

• Within-subject correlations: Standard dynamic functional connectivity

• ISFC (Inter-Subject Functional Connectivity): Shared patterns across subjects

• WISFC (Weighted ISFC): Similarity-weighted multi-subject analysis

• Auto-correlation functions: Temporal structure analysis

Dimensionality Reduction

• PCA: Principal component analysis for correlation patterns

• ICA: Independent component analysis

• Factor Analysis: Latent factor modeling

• Graph measures: Network centrality and connectivity metrics

Advanced Topics

• Higher-order correlations: Correlations between correlation patterns

• Multi-level analysis: Hierarchical temporal structure

• Statistical testing: Permutation tests and multiple comparisons

• Optimization: Memory and performance considerations

Common Use Cases

Neuroscience Applications

# Analyze brain network dynamics
brain_data = load_fmri_data()  # Shape: (timepoints, brain_regions)

# Compute dynamic functional connectivity
dfc = tc.timecorr(brain_data,
                  weights_function=tc.gaussian_weights,
                  weights_params={'var': 8})

# Visualize connectivity at specific timepoint
connectivity_matrix = tc.vec2mat(dfc[100, :])

Financial Market Analysis

# Analyze market correlations over time
stock_returns = load_market_data()  # Shape: (days, stocks)

# Compute dynamic correlations
market_correlations = tc.timecorr(stock_returns,
                                 weights_function=tc.laplace_weights,
                                 weights_params={'scale': 5})

Climate Science

# Study climate variable relationships
climate_data = load_climate_measurements()  # Shape: (months, variables)

# Analyze long-term correlation patterns
climate_correlations = tc.timecorr(climate_data,
                                  weights_function=tc.gaussian_weights,
                                  weights_params={'var': 12})  # Annual scale

Running the Tutorials

To run the interactive tutorials locally:

# Navigate to the timecorr directory
cd /path/to/timecorr

# Start Jupyter notebook
jupyter notebook

# Open tutorials in docs/tutorial/ folder

Next Steps

After completing the tutorials, explore:

• API Reference: Detailed function documentation

• Example Gallery: Additional code examples and use cases

• Research Paper: Theoretical background and validation studies

• GitHub Repository: Latest updates and community contributions