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Spurious regressions between I(1) processes with long memory errors

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  • Nunzio Cappuccio
  • Diego Lubian

Abstract

In this paper we develop the asymptotic distribution theory for spurious regression between I(1) processes with long‐memory stationary errors. Our result departs from the standard results of Phillips (Understanding spurious regression in econometrics. J. Economet. 33 (1986), 311–40) in two respects. First, the limit theory we apply is based on a functional central limit theorem for stationary linear processes whose spectral density at frequency zero may diverge or collapse to zero. Second, different limit distributions may apply depending on the form of long memory exhibited by the error term. We also discuss the extension of our analyis to spurious regression with fitted intercept.

Suggested Citation

  • Nunzio Cappuccio & Diego Lubian, 1997. "Spurious regressions between I(1) processes with long memory errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(4), pages 341-354, July.
    • Handle: RePEc:bla:jtsera:v:18:y:1997:i:4:p:341-354
    DOI: 10.1111/1467-9892.00054
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    Cited by:

    1. D. Ventosa-Santaulària, 2009. "Spurious Regression," Journal of Probability and Statistics, Hindawi, vol. 2009, pages 1-27, August.
    2. Noriega Antonio E. & Ventosa-Santaulària Daniel, 2006. "Spurious Regression and Econometric Trends," Working Papers 2006-05, Banco de México.
    3. P. M. Robinson & M. Gerolimetto, 2006. "Instrumental variables estimation of stationary and non-stationary cointegrating regressions," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 291-306, July.
    4. Mármol, Francesc, 1999. "How spurious features arise in case of fractional cointegration," DES - Working Papers. Statistics and Econometrics. WS 6349, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Hassler, Uwe & Breitung, Jörg, 2002. "A Residual-Based LM Test for Fractional Cointegration," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 37318, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    6. Antonio E. Noriega & Daniel Ventosa‐Santaulària, 2007. "Spurious Regression and Trending Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 69(3), pages 439-444, June.
    7. Antonio E. Noriega & Daniel Ventosa-Santaularia, 2005. "Spurious regression under deterministic and stochastic trends," Department of Economics and Finance Working Papers EM200503, Universidad de Guanajuato, Department of Economics and Finance.
    8. Noriega Antonio E. & Ventosa-Santaulària Daniel, 2011. "A Simple Test for Spurious Regressions," Working Papers 2011-05, Banco de México.
    9. Manuel Gómez Zaldivar & Oscar Manjarrez Castro & Daniel Ventosa-Santaulària, 2009. "Regresión espuria en especificaciones dinámicas," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(1), pages 1-20, May.

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