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

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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
    Department of Economics, Universidad Francisco de Vitoria, 28223 Madrid, Spain)

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.

Suggested Citation

  • Guglielmo Maria Caporale & Luis Alberiko Gil-Alana, 2025. "A Fractional Integration Model and Testing Procedure with Roots Within the Unit Circle," Mathematics, MDPI, vol. 13(18), pages 1-21, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:18:p:2978-:d:1749586
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