As can be seen from Table 1 that if it is assumed that the time periods of IMF1, IMF2, IMF3 and IMF4 components are short period, medium period, medium-long period and long period, the rainfall, runoff and sediment have a good correlation in periodic changes. Specifically, rainfall, runoff, and sediment all have the same short-period change, and the periodic year is 2 to 5 years; In the medium period, though the changing periodic years of the three are different, there is little difference, among which the rainfall is 5-8 years, runoff is 6-9 years, and sediment is 5-10 years; There are great differences between rainfall, runoff and sediment in the medium-long period, among which the span of sediment change is large with 11-30 years, 29-30 years for runoff and 9-11 years for rainfall; In terms of the long-period scale, rainfall is 28 years, runoff is 32 years and sediment is 41 years; The redidual component shows the overall trend of rainfall, runoff, and sediment. The rainfall showed a decreasing trend from 1966 to 1981, and an increasing trend from 1982 to 2013, but both runoff and sediment showed a decreasing trend. It can be seen that rainfall, runoff and sediment all have a complex multi-time scale periodic change laws, but they have a good correlation in the short and the medium periods. However, from the medium-long period, the periods of rainfall, runoff, and sediment present different, but for their residuals, they show the better synchronization.

The original time series and components of rainfall, runoff and sediment in the source area of the Yellow River are tested by unit root test. Assuming that xi , zi andyi (i = 0, 1, 2, 3, 4, 5) are used to represent the CEEMDAN component of rainfall, runoff, and sediment, andx0 , z0 , andy0 are their original sequences respectively. The optimal lag order is determined by the AIC criterion, and the unit root test results are given in Table 2.

The test results are shown in Table 2. The ADF test values of the original time series of rainfall, runoff and sediment in the source area of the Yellow River are all larger than the critical value of t test, so they belong to non-stationary time series, but their first-order difference time series are stationary. Meanwhile, their CEEMDAN components are stationary.

Table 2 Unit root test results of the original time series and components