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

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  • Guglielmo Maria Caporale
  • Luis Alberiko Gil-Alana

Abstract

This paper puts forward a general statistical model in the time domain based on the concept of fractional integration. More specifically, in the proposed framework instead of imposing that the roots are strictly on the unit circle, we also allow them to be within the unit circle. This approach enables us to specify the time series in terms of its infinite past, with a rate of dependence between the observations much smaller than that produced by the classic I(d) representations. Both 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," CESifo Working Paper Series 11983, CESifo.
    • Handle: RePEc:ces:ceswps:_11983
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    References listed on IDEAS

    as
    1. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
    2. Gil-Alana, L. A. & Robinson, P. M., 1997. "Testing of unit root and other nonstationary hypotheses in macroeconomic time series," Journal of Econometrics, Elsevier, vol. 80(2), pages 241-268, October.
    3. Diebold, Francis X. & Rudebusch, Glenn D., 1989. "Long memory and persistence in aggregate output," Journal of Monetary Economics, Elsevier, vol. 24(2), pages 189-209, September.
    4. Guglielmo Maria Caporale & Luis A. Gil-Alana & Kefei You, 2022. "Stock Market Linkages between the Asean Countries, China and the US: A Fractional Integration/cointegration Approach," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 58(5), pages 1502-1514, April.
    5. Cecchetti, Stephen G & Lam, Pok-sang & Mark, Nelson C, 1990. "Mean Reversion in Equilibrium Asset Prices," American Economic Review, American Economic Association, vol. 80(3), pages 398-418, June.
    6. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    7. Luis A. Gil-Alana & Javier Hualde, 2009. "Fractional Integration and Cointegration: An Overview and an Empirical Application," Palgrave Macmillan Books, in: Terence C. Mills & Kerry Patterson (ed.), Palgrave Handbook of Econometrics, chapter 10, pages 434-469, Palgrave Macmillan.
    Full references (including those not matched with items on IDEAS)

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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