A note on fractional stochastic convergence

We show that a class of non-stationary stochastic processes exhibiting long-range dependence satisfies one definition of time series convergence proposed in the literature. We also show explicitly the relationship between two time series concepts convergence proposed in the literature. Furthermore, we assess income per capita convergence for a sample OECD of economies using time series based tests. When we allow income shocks to exhibit long-range dependence, generalizing previous specifications, we find ample evidence of pairwise convergence among OECD economies. This finding is contrary to the literature that uses unit roots and cointegration tests.