The time-series difference method was used to correct for serial autocorrelation.
In the first step, the algorithm subtracted the magnitude spectra (magnitude differences between spectral lines of same frequency bin) of consecutive measurements and calculated the absolute values of these differences (referred to as difference spectrum), resulting in a time series of difference spectra.
We now define three measures based on the set of local optima of the completion time series: the difference in time ( Δ time ) and completion ( Δ completion ) between two successive optima, and the time to the same level after a local maxima ( Δ s a m e l e v e l ) (for details see Figure 11).
We remind that the analyzed time series are differences of the magnetic field intensity measurements obtained from two different instruments onboard same satellite.
Unit root tests are not designed for such a task since they aim at investigating whether a time series is difference-stationary or trend-stationary and are not, therefore, predictability tests.
Fig. 3 Time series of differences in FFC CO2 emission cases (CARBONES and IEA) relative to the CDIAC case (a), and the resulting differences in land CO2 sinks estimated by 84-region inverse model (b) for East Asia (black line: CDIAC CARBONES; red line: CDIAC IEA).
Specifically, for (1) to (3), we use a Wilcoxon signed-rank test to test the statistical significance of difference between pairs of different time series, as well as difference between the values of time series of each group and zeros.
In Figure 3B, we plotted time series of the difference between the Ct values of tolC and M13, and we found the Ct value difference is almost constant (7∼8) throughout the whole growth period.
The RMS misfits also show a slight increase in size over the latter half of the time series, but the difference is not large over most of the data set.
However, by adding the mean diurnal Sq variation and the midnight value at the start of the day to both time series data, this difference between the modelled and measured variation in the EEJ geomagnetic signature is less pronounced and could be neglected.
The color vector of the initial image was subtracted from the color vectors of all subsequent images in order to construct a time series of color difference vectors.
