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Research on multivariate statistical analysis methods of rural economic dynamics in the context of digital countryside

Xuelei Zhang

Xuelei Zhang

Laiwu Vocational and Technical CollegeLaiwu, China
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Zhang, Xuelei
  
Sep 26, 2025
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Published Online: Sep 26, 2025
Received: Jan 24, 2025
Accepted: May 05, 2025
DOI: https://doi.org/10.2478/amns-2025-1053
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© 2025 Xuelei Zhang, published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1.

The AR root diagram of the VAR(3) model
The AR root diagram of the VAR(3) model

Figure 2.

Esponse to cholesky one S.D. innovations±2 S.E.
Esponse to cholesky one S.D. innovations±2 S.E.

Normalized cointeger vector

lnGDP lnDI lnFDI lnL C
1.00000 -0.365521 -0.125112 -0.092311 -4.362281
Standard error 0.04551 0.02775 0.02932
Logarithmic likelihood 165.5226

The johansen cointegral test results

Original hypothesis Maximum characteristic root (p value) The critical value of a significant level of 1% Trace statistics (p) The critical value of a significant level of 1%
Zero cointegral vector 53.29066(0.0000)* 34.94264 107.18813(0.0000)* 61.64493
At least one cointegral vector 28.69266(0.0062)* 26.74797 53.47109(0.0003)* 42.37507
At least two cointegral vector 15.86719(0.0721) 20.90672 24.66381(0.0105) 22.8413
At least three cointegral vector 8.87416(0.0312) 12.12043 8.97686(0.0322) 13.26284

Regression

Variable Coefficient Std.error T-Statistic Prob.
C -995.9902 277.5201 -3.631125 0.0006
Y(-1) 0.781522 0.062366 15.03522 0.0000
X1 0.195532 0.041552 4.826638 0.0000
X2 0.335698 0.076552 4.189552 0.0002
X3 0.621852 0.226594 2.750622 0.0079
X5 1.720026 0.625512 2.795512 0.0062
X6 -0.000192 5.01E-05 -3.78445 0.0002
AR(1) 0.335216 0.096622 3.785123 0.0009
R-squared= 0.998562 Prob(F-statistic) =0.000000 DW=2.005163

The analysis of the variance of the natural log of GDP(%)

Period S.E. GDP X1 X2 X3 X4 X5 X6
1 0.01464 100.0000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
2 0.02642 80.19756 1.89617 0.38904 0.01614 8.4983 7.82309 1.15286
3 0.04793 61.07213 1.79602 1.46392 0.21004 27.21808 7.34092 0.93649
4 0.09444 48.26298 6.05166 1.00878 2.33838 30.11781 10.77132 1.43688
5 0.04111 38.86444 6.89306 0.95321 10.51809 24.88367 15.31345 2.61018
6 0.07439 31.58043 5.14293 1.60678 15.9649 20.95409 21.90103 2.92125
7 0.07039 27.3731 5.23869 2.3259 15.48904 21.80547 25.31351 2.45179
8 0.09172 25.01815 5.40247 2.4154 13.97588 24.84384 26.36582 2.05364
9 0.11117 24.07645 4.93682 2.13853 13.07808 26.59145 27.30454 1.78482
10 0.06304 23.96772 4.5089 1.96726 12.36968 27.23405 28.1668 1.6897
11 0.1295 24.22285 4.29938 1.92374 11.50914 27.60699 28.81192 1.65327
12 0.05609 24.21947 4.15354 1.93988 11.17518 27.71136 29.21589 1.55658
13 0.09017 24.11485 4.43411 1.9123 11.2414 27.44178 29.28908 1.49808
14 0.10479 23.75325 5.0351 2.13766 11.50924 26.90724 29.11073 1.48679
15 0.09456 23.38903 5.35229 2.90684 1156786.9996 26.68382 28.63542 1.46943
16 0.10775 22.80885 5.51564 3.89579 11.26928 27.32772 27.80869 1.41112
17 0.14629 21.98509 5.84277 4.77636 10.74959 28.6756 26.63784 1.30445
18 0.11912 21.08472 6.33147 5.10996 10.36302 30.2377 25.64932 1.27842
19 0.09877 20.23258 6.71344 5.08929 10.04628 31.60989 25.03608 1.21295
20 0.11584 19.56506 6.998 4.91568 9.83756 32.63112 24.85332 1.28206
Cholesky Ordering:LNGDP LNC LNG lni LNNX Lntiv LNCS

Least squares OLS regression

Variable Coefficient Std.error T-Statistic Prob.
C -2133.652 444.6522 -4.730225 0.0000
X1 0.254331 0.073226 3.261251 0.0016
X2 1.465123 0.057223 26.03155 0.0000
X3 0.341162 0.352251 0.932651 0.3681
X4 11.23551 4.641622 3.820013 0.0005
X5 -2.953251 1.636952 -1.754662 0.0835
X6 -0.000265 8.12E-05 -3.026631 0.0035
R-squared= 0.992166 Prob(F-statistic) =0.000000 DW=0.669522

The ADF unit root test results of the sequence

Sequence Test type (c,t,n) ADF statistic Critical value(1%,5%,10%) P value Test conclusion
lnGDP (c,t,1) -2.950332 (4.2839, -3.64942, -3.18816) 0.3736 Uneven stability
ΔlnGDP (c,t,1) -2.658842 (4.43536, -3.6879, -3.22979) 0.1466 Uneven stability
Δ2lnGDP (c,t,0) -5.036151*** (4.51379, -3.66272, -3.27613) 0.0519 Smoothness
lnDI (c,t,2) -2.056326 (4.67817, -3.48604, -3.10642) 0.7093 Smoothness
ΔlnDI (c,t,1) -3.261152 (4.51428, -3.57928, -3.08134) 0.1344 Uneven stability
Δ2lnDI (c,t,2) -2.919522 (4.45497, -3.6862, -3.2658) 0.1442 Uneven stability
lnFDI (c,t,2) -3.584622* (4.44747, -3.69755, -3.11141) 0.1846 Smoothness
ΔlnFDI (c,t,0) -3.598455*** (4.38435, -3.68442, -3.16157) 0.0019 Uneven stability
Δ2lnFDI (c,t,3) -5.532632*** (4.52978, -3.71165, -3.19359) 0.0962 Smoothness
lnL (c,t,1) -2.362152 (4.44082, -3.40217, -3.14687) 0.1579
ΔlnL (c,t,0) -5.031162*** (4.46693, -3.70134, -3.22446) 0.0304 Smoothness
Δ2lnL (c,t,0) -6.952263*** (4.52884, -3.66022, -3.45295) 0.0001 Uneven stability

Granger causality test

Original hypothesis F statistic P value
Di is not the granger reason for GDP 6.75032*** 0.0038
GDP is not di’s granger reason 3.85562** 0.0349
FDI is not the granger reason for GDP 3.04122* 0.0637
GDP is not the reason for the granger of FDI 1.52155 0.2831
L is not the granger reason of GDP 5.88965*** 0.0072
GDP is not the granger reason for L 2.31662 0.1206
FDI is not di’s granger reason 3.95223** 0.0291
Di is not the reason for the granger of FDI 4.59211** 0.0185
L is not di’s granger reason 0.25705 0.8639
Di is not the granger reason for L 9.45112*** 0.0041
L is not the reason for the granger of FDI 2.63551* 0.0924
FDI is not the granger reason for L 1.28155 0.3154
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