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Spectral Regression For Cointegrated Time Series With Long‐Memory Innovations

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  • D. Marinucci

Abstract

Spectral regression is considered for cointegrated time series with long‐memory innovations. The estimates we advocate are shown to be consistent when cointegrating relationships among stationary variables are investigated, while ordinary least squares are inconsistent due to correlation between the regressors and the cointegrating residuals; in the presence of unit roots, these estimates share the same asymptotic distribution as ordinary least squares. As a corollary of the main result, we provide a functional central limit theorem for quadratic forms in non‐stationary fractionally integrated processes.

Suggested Citation

  • D. Marinucci, 2000. "Spectral Regression For Cointegrated Time Series With Long‐Memory Innovations," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(6), pages 685-705, November.
    • Handle: RePEc:bla:jtsera:v:21:y:2000:i:6:p:685-705
    DOI: 10.1111/1467-9892.00204
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    Citations

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    Cited by:

    1. Peter M Robinson, 2004. "The Distance between Rival Nonstationary Fractional Processes," STICERD - Econometrics Paper Series 468, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, Department of Economics and Business Economics, Aarhus University.
    3. Robinson, Peter M., 2004. "The distance between rival nonstationary fractional processes," LSE Research Online Documents on Economics 2282, London School of Economics and Political Science, LSE Library.
    4. Javier Hualde & Fabrizio Iacone, 2015. "Small-b and Fixed-b Asymptotics for Weighted Covariance Estimation in Fractional Cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(4), pages 528-540, July.
    5. Lasak, Katarzyna, 2010. "Likelihood based testing for no fractional cointegration," Journal of Econometrics, Elsevier, vol. 158(1), pages 67-77, September.
    6. Robinson, P.M., 2005. "The distance between rival nonstationary fractional processes," Journal of Econometrics, Elsevier, vol. 128(2), pages 283-300, October.
    7. Avarucci, Marco & Marinucci, Domenico, 2005. "Polynomial cointegration among stationary processes with long memory," UC3M Working papers. Economics we055123, Universidad Carlos III de Madrid. Departamento de Economía.
    8. Uwe Hassler & Francesc Marmol & Carlos Velasco, 2008. "Fractional cointegration in the presence of linear trends," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 1088-1103, November.
    9. Christensen, Bent Jesper & Nielsen, Morten Orregaard, 2006. "Asymptotic normality of narrow-band least squares in the stationary fractional cointegration model and volatility forecasting," Journal of Econometrics, Elsevier, vol. 133(1), pages 343-371, July.
    10. Marinucci, D. & Robinson, Peter M., 2001. "Narrow-band analysis of nonstationary processes," LSE Research Online Documents on Economics 303, London School of Economics and Political Science, LSE Library.
    11. Banerjee, Anindya & Urga, Giovanni, 2005. "Modelling structural breaks, long memory and stock market volatility: an overview," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 1-34.
    12. Morten Ø. Nielsen & Per Houmann Frederiksen, 2008. "Fully Modified Narrow-band Least Squares Estimation Of Stationary Fractional Cointegration," Working Paper 1171, Economics Department, Queen's University.
    13. Davidson, James, 2002. "A model of fractional cointegration, and tests for cointegration using the bootstrap," Journal of Econometrics, Elsevier, vol. 110(2), pages 187-212, October.

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