Assessing spatio-temporal coupling between intangible cultural heritage and rural development in China (2013–2022) through coupling coordination analysis and random-forest prediction

This study analyzes panel data from 31 provinces in China spanning 2013 to 2022, employing the entropy value approach and the coupling coordination degree model to assess the coupling coordination level between intangible cultural heritage and rural development. Data sourced from the China Cultural Heritage and Tourism Statistical Yearbook, the National Bureau of Statistics of China, and other official data. This study analyzes the dynamic development and spatial relationship between the two with the help of the Moran’s I index, kernel density estimation, and Markov chains. Second, using the variable indicators of both as targets, a random forest model was employed to predict the results. Stability recommendations were derived by altering the number of seeds and splitting the training set. The results indicate the following: (1) Analysis of the coupling model reveals that the coordination level between intangible cultural heritage and rural development exhibits a high degree of alignment. Spatially, the results show a pattern of “higher in the east, lower in the west, with central and northeastern regions in between” across provinces. (2) The Moran’s I index indicates stable spatial hierarchy, though it also generates mobility similar to other adjacent tiers. (3) The kernel density model shows narrowing and widening states after peaking in 2022, revealing a trend of diminishing differentiation. (4) The random forest analysis demonstrates that intangible cultural heritage inheritors rank first in density metrics. Both indicators will continue to show positive growth, albeit at high speeds with slow development margins.