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With the EU Green Deal initiatives, European members seek to launch the first climate neutral continent by 2050. This paper assesses the stochastic convergence of per capita energy consumption series for an illustrative sample of 15 EU countries with memberships prior to the 2004 enlargement, using data spanning the 1970–2018 period. Results from the confidence interval subsampling (asymmetric and equal-tailed) highlight that 11 out of the 15 EU series exhibit a long-run memory behaviour, while a diverging pattern was observed for the UK, Germany, Portugal, and Italy. Finally, per capita energy use series persist but fail to reveal one of the above dynamics for Ireland and Spain. Also, findings from the non-parametric Bayesian application (ANOVA/linear Dependent Dirichlet Process (DDP) mixture model) show how economic growth operates as a converging energy consumption-enabler over the long-run, from which the EU membership cannot be excluded. In particular, we highlight how the nature of energy-GDP hypotheses vary with the stochastic properties of energy use (converging behaviour with temporary shocks, converging pattern with permanent shocks, and diverging dynamic). Finally, our conclusions overcome the well-established development stage argument as we claim that countries with similar energy convergence patterns may need to adopt similar energy policies. [ABSTRACT FROM AUTHOR]