# Spatial–temporal coupling coordination and interaction between … – Nature.com ### Spatial–temporal evolution of coordination degree between digitalization and traditional industrial upgrading in the Yellow River Basin

#### The temporal evolution characteristics of the coordination degree between digitalization and traditional industrial upgrading in the Yellow River Basin

Furthermore, the non-parametric kernel density estimation method based on kernel function is employed to investigate the dynamic change trend of the coordination degree between digitalization and traditional industrial upgrading in the Yellow River Basin. The basic principle is as follows: Let X1, X2, …, Xn follows the same distribution, and its probability density f(x) must be obtained by sample estimation. Sample empirical distribution function F(X) is shown in Formula (21).

$$F\left( x \right) = \frac{1}{n}\left\{ {x_{1} ,x_{{2}} , \ldots ,x_{n} } \right\}$$

(21)

The probability density estimation of fixed bandwidth is shown in Formula (22).

$$f\left( x \right) = \frac{{\left[ {F\left( {x + h_{n} } \right) – F\left( {x – h_{n} } \right)} \right]}}{2h} = \int_{{x – h_{n} }}^{{x + h_{n} }} {\frac{1}{h}K\left( {\frac{t – x}{{h_{n} }}} \right)} dF_{n} \left( t \right) = \frac{1}{{nh_{n} }}\sum\limits_{i = 1}^{n} {K\left( {\frac{{x – x_{i} }}{{h_{n} }}} \right)}$$

(22)

where n is the number of samples, h is the bandwidth, and $$K\left( \cdot \right)$$ is the kernel function. In order to maximize the fitting effect, the commonly utilized Epanechnikov kernel function was selected, and the data-based automatic bandwidth was further selected according to the principle of minimum mean square error72.

#### The spatial evolution characteristics of coordination degree between digitalization and traditional industrial upgrading in the Yellow River Basin

Due to more intuitively observe the spatial characteristics of the coupling coordination degree in each region of the Yellow River basin, this paper draws the global Moran’s I index table and the local Moran’s I index scatter chart of the nine provinces of the Yellow River Basin on the basis of the economic distance weight matrix. According to Table 6, the Moran’s I index of the coordination degree between digitalization and traditional industrial upgrading in the Yellow River Basin during the sample observation period is all positive, and the empirical results show that there is a positive spatial correlation between digitalization and traditional industrial upgrading coordination in the Yellow River Basin. The coupling coordination level of digitalization and traditional industrial upgrading among provinces is closely related to the coupling coordination level of neighboring regions, which is shown as a relatively stable spatial clustering feature.

### Interactive mechanism between digitalization and traditional industrial upgrading in the Yellow River Basin

#### Regression results of stationarity test, co-integration test and lag order selection

A prerequisite for the application of panel VAR model is the stationarity and co-integration relationship between variables. Therefore, this paper selected Fisher-ADF test and LLC test to test the common and individual unit roots. In addition, Fisher ADF and Fisher PP tests were also used to make the test results more accurate. The test results in Table 7 show that all ten variables are first-order unitary. On this basis, Kao test is continued to verify the co-integration relationship between variables. The panel co-integration test results of the two models are listed in Table 8, and the results show that there is a co-integration relationship between variables at the significance level of 1% and 5%. The panel VAR model can be consequently selected to examine the interactive relationship between digitalization and the traditional industrial upgrading. In addition, the length of the lag order is related to the accuracy of the estimated results, and the determination of the lag order is the second prerequisite for the application of the panel VAR model. In particular, the loss of degrees of freedom will bring significant deviation to the empirical results under the small samples in this paper. It lists the test results of lag order according to the commonly exploited AIC, BIC and HQIC criteria in Table 9, and the results show that the selection of second-order lag panel VAR model is more reasonable.

#### Analysis on the interactive effect of digitalization and traditional industrial upgrading in the Yellow River Basin

The impulse response function of panel VAR model can quantitatively describe the current and future impacts of an endogenous variable on other endogenous variables after applying an orthogonalization pulse of one standard deviation, and obtain the dynamic correlation features between the two endogenous variables while other endogenous variables are controlled. Furthermore, the dynamic interaction effect between digitalization level and traditional industrial upgrading can be more thoroughly observed by impulse response function graph based on the interaction characteristics of describing variables. The first step is to obtain the impulse response function by Cholesky decomposition. The second step is to run 300 simulations through Monte Carlo method to obtain a confidence interval of two standard deviations. The horizontal and vertical axes in Figs. 6 and 7 respectively represent the number of lag periods (s) and the impulse response value. The red and black solid lines represent the impulse response curve and the 95% confidence interval, respectively76.

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