Table 1 Stationarity test of time series (x_t) using the Augmented Dickey-Fuller (ADF) test, including decomposed approximate coefficients for four flood indices, global mean temperature, China’s precipitation regime, and population, forest cover, and polder area in the Yangtze River Basin from 950 to 2000 CE

ADF t-statistic	Constant, Linear trend			Constant			None			Order of integration
ADF t-statistic	x_t	∆x_t	∆²x_t	x_t	∆x_t	∆²x_t	x_t	∆x_t	∆²x_t	Order of integration
Annual flood sum	−0.2850	−9.6753(***)		1.7991	−9.0177 (***)		2.4303	−8.6825 (***)		I(1)
Annual flooded basin	0.9908	−9.1460 (***)		2.4348	−8.3322 (***)		2.9789	−7.9742 (***)		I(1)
Overall flood intensity	−3.1266	−9.1092 (***)		−0.7714	−8.9627 (***)		0.1713	−8.8672 (***)		I(1)
100-year flood density	−1.8412	−28.0179 (***)		1.1138	−27.8932 (***)		2.8500	−27.6763 (***)		I(1)
Global mean temperature (T)	−2.3068	−21.4404 (***)		−2.4386	−21.3905 (***)		0.4737	−21.3904 (***)		I(1)
Precipitation regime (P)	−27.4758 (***)	−21.0486 (***)		−27.4608 (***)	−21.0589 (***)		−1.5759	−21.0689 (***)		I(1)
Population (Po)	0.2468	−1.9118	−32.3913 (***)	1.8517	−0.9615	−32.3657 (***)	2.1770	−0.3983	−32.3570 (***)	I(2)
Forest cover (Fc)	0.2287	0.5898	−34.8369 (***)	−1.7736	0.9403	−34.7077 (***)	0.5492	0.6289	−34.6776 (***)	I(2)
Polder area (Pa)	−2.6983	−3.8077 (*)		-1.3877	-3.7119 (**)		1.3171	-2.9702 (**)		I(1)

The null hypothesis assumes that x_t has a unit root, with the regression method being ordinary least squares (OLS) and three options for an exogenous regressor: (1) constant and linear trend, (2) constant, and (3) none. The ADF test is applied to x_t and its higher-order differences until the t-statistic becomes significant, which determines the order of integration for the series. The results indicate that all series are nonstationary I(1) processes, except for population and forest cover, which are I(2) processes.
(***), (**), and (*) denote the test significance at the level of p < 0.001, <0.01, and <0.05, respectively.

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