Long-range cross-correlation between heart rate and physical activity in daily life

To characterize long-range cross-correlation in nonstationary bi-variate time series, we propose the higherorder detrending moving-average cross-correlation analysis (DMCA) in which the Savitzky-Golay (S-G) filters are employed as the detrending operator and show its methodological properties analytically. Using the higher-order DMCA, time series consisting of heart rate (HR) and physical activity measured in daily life were analyzed. Our analysis demonstrated that the daily physical activity shared a common long-range correlated factor with the
$1/f$
-type fluctuation of HR.