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Diagnostic Testing For Cointegration

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  • Peter Robinson
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    Abstract

    We develop a sequence of tests for specifying the cointegrating rank of, possiblyfractional, multiple time series. Memory parameters of observables are treated asunknown, as are those of possible cointegrating errors. The individual test statisticshave standard null asymptotics, and are related to Hausman specification teststatistics: when the memory parameter is common to several series, an estimate ofthis parameter based on the assumption of no cointegration achieves an efficiencyimprovement over estimates based on individual series, whereas if the series arecointegrated the former estimate is generally inconsistent. However, acomputationally simpler but asymptotically equivalent approach, which avoidsexplicit computation of the "efficient" estimate, is instead pursued here. Twoversions of it are initially proposed, followed by one that robustifies to possibleinequality between memory parameters of observables. Throughout, asemiparametric approach is pursued, modelling serial dependence only atfrequencies near the origin, with the goal of validity under broad circumstances andcomputational convenience. The main development is in terms of stationary series,but an extension to nonstationary ones is also described. The algorithm forestimating cointegrating rank entails carrying out such tests based on potentially allsubsets of two or more of the series, though outcomes of previous tests mayrender some or all subsequent ones unnecessary. A Monte Carlo study of finitesample performance is included.

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    Bibliographic Info

    Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2007/522.

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    Date of creation: Sep 2007
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    Handle: RePEc:cep:stiecm:/2007/522

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    Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

    Related research

    Keywords: Fractional cointegration; Diagnostic testing; Specificationtesting; Cointegrating rank; Semiparametric estimation.;

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    References

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    1. D Marinucci & Peter M Robinson, 2001. "Semiparametric Fractional Cointegration Analysis," STICERD - Econometrics Paper Series /2001/420, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. Velasco, Carlos, . "Gaussian Semiparametric Estimation of Non-stationary Time Series," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4345, Universidad Carlos III de Madrid.
    3. Giraitis, L. & Robinson, P.M., 2003. "Edgeworth expansions for semiparametric Whittle estimation of long memory," Open Access publications from London School of Economics and Political Science http://eprints.lse.ac.uk/, London School of Economics and Political Science.
    4. Robinson, Peter M. & Yajima, Yoshihiro, 2002. "Determination of cointegrating rank in fractional systems," Journal of Econometrics, Elsevier, vol. 106(2), pages 217-241, February.
    5. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
    6. Katsumi Shimotsu, 2006. "Gaussian Semiparametric Estimation of Multivariate Fractionally Integrated Processes," Working Papers 1062, Queen's University, Department of Economics.
    7. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    8. Lobato, Ignacio N., 1999. "A semiparametric two-step estimator in a multivariate long memory model," Journal of Econometrics, Elsevier, vol. 90(1), pages 129-153, May.
    9. Liudas Giraitis & Peter M Robinson, 2002. "Edgeworth Expansions for Semiparametric Whittle Estimation of Long Memory," STICERD - Econometrics Paper Series /2002/438, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    10. Hausman, Jerry A, 1978. "Specification Tests in Econometrics," Econometrica, Econometric Society, vol. 46(6), pages 1251-71, November.
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    Cited by:
    1. Phillips, Peter C.B., 2009. "Long memory and long run variation," Journal of Econometrics, Elsevier, vol. 151(2), pages 150-158, August.

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