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

Guglielmo Maria Caporale () and Luis Alberiko Gil-Alana
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Guglielmo Maria Caporale: Department of Economics, Finance and Accounting, Brunel University of London, London UB8 3PH, UK
Luis Alberiko Gil-Alana: Faculty of Economics, University of Navarra, 31009 Pamplona, Spain

Mathematics, 2025, vol. 13, issue 18, 1-21

Abstract: 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.

Keywords: fractional integration; unit roots; testing procedure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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