A Hybrid Multilayer Dynamic Modelling Framework for Path-Dependent Stochastic Systems: Application to EU Digital Public Services

Path-dependent dynamic systems are often analysed through separate metric, stochastic, econometric or nonlinear methods, while their integration within a unified architecture remains limited. This study develops and validates a Hybrid Dynamic Modelling Framework (HDMF) for path-dependent stochastic systems, using EU-27 digital public service trajectories during 2017–2022 as an empirical application. The framework combines DTW-TimeSeriesKMeans clustering, Markov transition analysis, PVAR, SEM and MLP approximation. The findings answer the four research questions sequentially. First, EU digital public service development is represented by three distinct trajectory regimes rather than a single convergence path. Second, the Markov layer shows strong diagonal dominance, limited mobility and practical non-ergodicity over the finite observation horizon, indicating persistent state dependence. Third, the PVAR layer confirms dynamic stability and bounded feedback within the institutional–digital system. Fourth, the SEM and MLP layers identify governance as a coherent latent institutional structure and reveal nonlinear predictive heterogeneity, suggesting possible threshold-type behaviour. Overall, the findings support the HDMF as a coherent multilayer architecture for modelling complex path-dependent systems and demonstrate its empirical usefulness through the EU digital public service case.