Before revision:  A comparison with the sliding window Pearson correlation of the raw time series in several stationary and non-stationary set-ups do not indicate any  mathematical advantages of the proposed metric over commonly used correlation methods .
After revision:  A comparison with the sliding window Pearson correlation of the raw time series in several stationary and non-stationary set-ups , including a realistic stationary network detection, reveals lower sensitivity of derivatives to low frequency drifts and to autocorrelations but also lower signal-to-noise ratio. It does not indicate any mathematical advantages of the proposed metric over commonly used correlation methods .