A Fractional Integration Model and Testing Procedure with Roots Within the Unit Circle

In this paper we propose a statistical model that combines both autoregressions and fractional differentiation in a unified treatment. However, instead of imposing that the roots are strictly on the unit circle, we also allow them to be within the unit circle. This permits a higher degree of flexibility in the specification of the model, with rates of dependence combining exponential with hyperbolic decays. Monte Carlo experiments and empirical applications to climatological and financial data show that the proposed approach performs well.