Note: In the test type (c, t, k), c is the intercept item, t is the time trend term (t=0 means no trend) and k is the optimal lag length.
  1. Co-integration Test
Co-integration test is conducted on their original time series and CEEMDAN decomposition sequence of rainfall, runoff and sediment with EG two-step method. The first step is to perform OLS regression on the original sequence and the same time scale component sequence of rainfall, runoff, sediment to establish a co-integration equation; the second step is to perform a unit root test on the residuals of each co-integration equation. If the residual sequence is stationary, the co-integration relationship exists; otherwise this relationship does not exist. It can be seen from table 3 that the ADF test values of the residual sequences of all co-integration equations are less than the critical values of the significance levels of 1%, 5% and 10%, so the co-integration relationship exists.
(11)
(0.014418) (0.005056)
(12)
(0.071956) (0.005192)
(13)
(0.094843) (0.004324)
(14)
(0.220190) (0.017521)
(15)
(0.025683) (0.002785)
(16)
(0.001172) (0.000456)
In the formula, ut represents the residual sequence of the equation, and the data in bracket is the standard deviation of the corresponding coefficient of the equation.
Table 3 Unit root test results of residual sequences of co-integration equations