Surrogate data analysis for assessing the significance of the coherence function

Area of Science:

• Cardiovascular Physiology
• Time Series Analysis
• Biomedical Signal Processing

Background:

• Assessing coupling between cardiovascular time series is crucial.
• Traditional coherence function thresholds may be unreliable due to series-specific features.
• Existing methods often fail to account for spurious coherence.

Purpose of the Study:

• To compare three surrogate data methods for setting reliable coherence thresholds.
• To evaluate the effectiveness of surrogate data in avoiding false coupling detections.
• To recommend optimal methods for cardiovascular variability analysis.

Main Methods:

• Generation of three types of surrogate time series: independent identically distributed (IID), Fourier transform (FT), and autoregressive (AR).
• Validation of surrogate methods using computer simulations of cardiovascular interactions.
• Comparison of frequency-dependent thresholds derived from different surrogate types.

Main Results:

• IID surrogate thresholds depended only on record length and estimator parameters.
• FT and AR surrogate thresholds were frequency-dependent, showing peaks at local coherence maxima.
• FT and AR surrogates effectively compensated for spurious coherence peaks from independent oscillations.
• Frequency-dependent thresholds proved beneficial for short series with narrow-band oscillations.

Conclusions:

• Surrogate methods preserving the power spectrum (FT and AR) are superior for setting coherence thresholds.
• These methods prevent false coupling detections in cardiovascular and cardiorespiratory regulation.
• Recommended for analyzing short time series with potential for independent, nearby frequency oscillations.