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  • Rxy(τ)=1Nt−1∑tNt−τ(x(t+τ)−x¯)(y(t)−y¯)σxσy(1)The linear trend of time series signals (x(t) and y(t)) was excluded using the “detrend” function of MATLAB (The MathWorks Inc, USA) and the signals were filtered using Hanning windows of the same size as the data length before their cross correlation was calculated (the MATLAB’s “detrend” function computes the least-squares fit of a straight line to the data in question and subtracts the resulting function from the data). Prior to model estimation, time series data were resampled to 5 Hz (40-point down-sampling using the “decimate” function of MATLAB to have appropriate time intervals of the estimation (the MATLB’s “decimate” function applies a 30th order, low-pass finite impulse response (FIR) filter to the original time series for data resampling).
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