Time series data from Assessment of long-range cross-correlations in cardio-respiratory and cardiovascular interactions

We propose higher-order detrending moving-average cross-correlation analysis (DMCA) to assess the long-range cross-correlations in cardio-respiratory 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 cardio-respiratory and cardiovascular time series analysis. In the cardio-respiratory 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’.