We propose higher-order detrending moving-average cross-correlation analysis (DMCA) to assess the long-range cross-correlations in cardiorespiratory and cardiovascular interactions. Although the original (zeroth-order) DMCA employs a simple moving-average detrending filter to remove non-stationary trends embedded in the observed time series, our approach incorporates a Savitzky-Golay filter as a higher-order detrending method. Because the non-stationary trends can adversely affect the long-range correlation assessment, the higher-order detrending serves to improve accuracy. To achieve a more reliable characterization of the long-range cross-correlations, we demonstrate the importance of the following steps: correcting the time scale, confirming the consistency of different order DMCAs, and estimating the time lag between time series. We applied this methodological framework to cardiorespiratory and cardiovascular time series analysis. In the cardiorespiratory interaction, respiratory and heart rate variability (HRV) showed long-range auto-correlations; however, no factor was shared between them. In the cardiovascular interaction, beat-to-beat systolic blood pressure and HRV showed long-range auto-correlations and shared a common long-range, cross-correlated factor. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.
Keywords: complex system interaction; cross-spectral analysis; long memory process.