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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

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Granger causality analysis with nonuniform sampling and its application to pulse-coupled nonlinear dynamics.

Yaoyu Zhang¹, Yanyang Xiao¹, Douglas Zhou¹

¹Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China.

Physical Review. E

|May 14, 2016

Summary

Nonuniform sampling improves Granger causality (GC) analysis for time series data. This method overcomes aliasing issues common with uniform sampling, enabling reliable causal inference even at lower rates in nonlinear networks.

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Area of Science:

Time Series Analysis
Causal Inference
Nonlinear Dynamics

Background:

Granger causality (GC) is vital for time series causal inference.
Uniform sampling can cause aliasing, leading to unreliable GC results.
High sampling rates are traditionally needed to mitigate this.

Purpose of the Study:

To develop a reliable GC analysis framework for nonuniformly sampled time series.
To address the unreliability of traditional GC in the presence of aliasing.
To enable accurate causal inference in nonlinear networks with limited sampling.

Main Methods:

Developed an unbiased power spectral density estimation for nonuniformly sampled data.
Established a spectrum-based nonparametric GC analysis framework.
Applied the framework to pulse-coupled nonlinear networks.

Main Results:

Nonuniform sampling effectively mitigates aliasing issues in GC analysis.
The proposed framework achieves reliable GC inference at low nonuniform mean sampling rates.
Demonstrated accurate causal inference in nonlinear networks where uniform sampling fails.

Conclusions:

Nonuniform sampling offers a robust solution for reliable Granger causality inference.
The spectrum-based GC framework is effective for complex nonlinear systems.
This approach enhances causal discovery in real-world, irregularly sampled data.