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West African countries have long promoted economic integration and income convergence. In recent trends, Nigeria has recorded the highest GDP per capita, and its neighbouring countries are yet to catch up with this economic growth. The paper examines the convergence of West African countries to catch up with Nigeria in terms of real per capita income. For the estimation, the paper employs fractional unit root approach to model simultaneously smooth breaks by means of flexible Fourier function in time. This approach is novel and has not been widely applied in the study of economic convergence across countries. The findings show that, while there is evidence of economic convergence and catching up in West Africa, only Ghana is likely to catch up with Nigeria in the region. As a policy recommendation, the West African countries should strengthen their human resource capacities through acquisition of relevant skills and technology transfers. This would promote income convergence and equitable economic growth. • Fractional unit root test with smooth Fourier function. • A new time series econometric approach for investigating economic convergence. • Economic convergence of West African states. • Ghana is likely to catch up economically with Nigeria in terms of Per capita Output in the future. [ABSTRACT FROM AUTHOR]