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The Stochastic Unit Root Model And Fractional Integration: An Extension To The Seasonal Case


  • Guglielmo Maria Caporale


  • Luis A. Gil-Alana


In a recent paper, Yoon (2003) shows that the Stochastic Unit Root (STUR) model is closely related to long memory processes, and, in particular, that it is a special case of an I(d) process, with d = 1.5. In this paper we further examine this issue by using parametric and semiparametric techniques for modelling long memory. In particular, we extend the analysis by considering both non-normality and seasonality, and shed light, theoretically and by means of Monte Carlo methods, on the relationship between the seasonal STUR and the seasonal I(d) models. The results show that, even in the case of I(1.5) underlying processes, the methods, which are specifically designed for testing I(d) statistical models are not appropriate for testing the STUR model. Moreover, they have in some cases very low power against STUR alternatives.

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  • Guglielmo Maria Caporale & Luis A. Gil-Alana, 2004. "The Stochastic Unit Root Model And Fractional Integration: An Extension To The Seasonal Case," Economics and Finance Discussion Papers 04-15, Economics and Finance Section, School of Social Sciences, Brunel University.
  • Handle: RePEc:bru:bruedp:04-15

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    References listed on IDEAS

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    5. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-596, May.
    6. He, Changli & Ter svirta, Timo, 1999. "FOURTH MOMENT STRUCTURE OF THE GARCH(p,q) PROCESS," Econometric Theory, Cambridge University Press, vol. 15(06), pages 824-846, December.
    7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    8. Davidson, James, 2002. "Establishing conditions for the functional central limit theorem in nonlinear and semiparametric time series processes," Journal of Econometrics, Elsevier, vol. 106(2), pages 243-269, February.
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