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A Residual-Based Lm-Type Test Against Fractional Cointegration

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  • Hassler, Uwe
  • Breitung, Jörg

Abstract

Nonstationary integrated time series may be fractionally cointegrated. Here we propose a test for the null hypothesis of no cointegration. It builds on the asymptotically normal Lagrange multiplier (LM) test against fractional alternatives applied to single equation residuals. It is shown that the LM test applied naively to residuals from a static level regression does not retain asymptotic normality. However, when the LM statistic is employed with residuals from a regression of differenced variables, then the test statistic is shown to have a standard normal limiting distribution. Monte Carlo experiments establish its relevance in finite samples.We thank Norbert Christopeit and three anonymous referees for corrections and very valuable comments.

Suggested Citation

  • Hassler, Uwe & Breitung, Jörg, 2006. "A Residual-Based Lm-Type Test Against Fractional Cointegration," Econometric Theory, Cambridge University Press, vol. 22(6), pages 1091-1111, December.
    • Handle: RePEc:cup:etheor:v:22:y:2006:i:06:p:1091-1111_06
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    Citations

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    Cited by:

    1. Uwe Hassler & Matei Demetrescu & Adina Tarcolea, 2011. "Asymptotic normal tests for integration in panels with cross-dependent units," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(2), pages 187-204, June.
    2. Uwe Hassler & Barbara Meller, 2014. "Detecting multiple breaks in long memory the case of U.S. inflation," Empirical Economics, Springer, vol. 46(2), pages 653-680, March.
    3. Uwe Hassler & Paulo M.M. Rodrigues & Antonio Rubia, 2016. "Quantile Regression for Long Memory Testing: A Case of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 14(4), pages 693-724.
    4. Christian Leschinski & Michelle Voges & Philipp Sibbertsen, 2021. "A comparison of semiparametric tests for fractional cointegration," Statistical Papers, Springer, vol. 62(4), pages 1997-2030, August.
    5. Nielsen, Morten Orregaard & Shimotsu, Katsumi, 2007. "Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 574-596, December.
    6. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    7. Lasak, Katarzyna, 2010. "Likelihood based testing for no fractional cointegration," Journal of Econometrics, Elsevier, vol. 158(1), pages 67-77, September.
    8. Paulo M.M. Rodrigues & Philipp Sibbertsen, 2019. "Testing for breaks in the cointegrating relationship: On the stability of government bond markets’ equilibrium," Working Papers w201912, Banco de Portugal, Economics and Research Department.
    9. Jorge M. L. Andraz & Raúl F. C. Guerreiro & Paulo M. M. Rodrigues, 2018. "Persistence of travel and leisure sector equity indices," Empirical Economics, Springer, vol. 54(4), pages 1801-1825, June.
    10. Avarucci, Marco & Velasco, Carlos, 2009. "A Wald test for the cointegration rank in nonstationary fractional systems," Journal of Econometrics, Elsevier, vol. 151(2), pages 178-189, August.
    11. Martins, Luis F. & Rodrigues, Paulo M.M., 2014. "Testing for persistence change in fractionally integrated models: An application to world inflation rates," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 502-522.
    12. Demetrescu, Matei & Kusin, Vladimir & Salish, Nazarii, 2022. "Testing for no cointegration in vector autoregressions with estimated degree of fractional integration," Economic Modelling, Elsevier, vol. 108(C).

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