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Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
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Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method
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Inferring directed spectral information flow between mixed-frequency time series.

Qiqi Xian, Zhe Sage Chen

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    Summary

    This study introduces a new method, Mixed-Frequency Time-Frequency Canonical Correlation Analysis (MF-TFCCA), to detect spectral information flow in complex datasets. MF-TFCCA accurately identifies directed information flow and driving frequencies, outperforming traditional models.

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    Area of Science:

    • Time series analysis
    • Nonlinear dynamics
    • Information theory

    Background:

    • Directed spectral information flow is crucial in fields like finance, climate, and neuroscience.
    • Traditional methods like Vector Autoregressive (VAR) models struggle with mixed frequencies and nonlinearities.
    • Spectral Granger Causality (SGC) quantifies directed information flow at specific frequencies.

    Purpose of the Study:

    • To develop a novel, non-parametric approach for assessing spectral information flow in multivariate time series with mixed frequencies and nonlinear interactions.
    • To introduce the Mixed-Frequency Time-Frequency Canonical Correlation Analysis (MF-TFCCA) method.
    • To evaluate the performance and efficiency of MF-TFCCA against existing models.

    Main Methods:

    • Developed the Mixed-Frequency Time-Frequency Canonical Correlation Analysis (MF-TFCCA) approach.
    • Validated MF-TFCCA using extensive computer simulations on mixed-frequency time series with varying interaction complexities.
    • Assessed statistical significance using surrogate data analysis.
    • Benchmarked MF-TFCCA against the parametric Mixed-Frequency Vector Autoregressive (MF-VAR) model.

    Main Results:

    • MF-TFCCA demonstrated superior computational efficiency and detection accuracy compared to the MF-VAR model.
    • The method successfully identified the strength and dominant driving frequencies of spectral information flow.
    • MF-TFCCA proved effective in analyzing real-world data from finance, climate, and neuroscience.

    Conclusions:

    • MF-TFCCA offers a robust, computationally efficient, and non-parametric framework for quantifying directed information flow in complex, nonlinear, mixed-frequency time series.
    • The approach enhances the analysis of interconnected systems across various scientific domains.
    • MF-TFCCA provides a valuable tool for exploratory data analysis in finance, climate science, and neuroscience.