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Multivariate Lagrange Multiplier Tests for Fractional Integration

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  • Nielsen, Morten Oe.

    (Department of Economics, University of Aarhus, Denmark)

Abstract

We introduce a multivariate Lagrange Multiplier (LM) test for fractional integration. We derive and analyze the LM statistic and show that it is asymptotically chi-squared distributed under local alternatives, and that, under Gaussianity, the LM test is asymptotically efficient against local alternatives. It is shown that the regression variant in Breitung & Hassler (2002, Journal of Econometrics 110, 167-185) is not equivalent to the LM test in the multivariate case, although it is in the univariate case. A generalization of the LM test that explicitly allows for different integration orders for each variate is also introduced. The finite sample properties of the LM test are evaluated and compared to the Breitung & Hassler (2002) test by Monte Carlo experiments. An application to multivariate time series of real interest rates for six countries is offered, demonstrating that more clear-cut evidence can be drawn from multivariate tests compared to conducting several univariate tests.

Suggested Citation

  • Nielsen, Morten Oe., "undated". "Multivariate Lagrange Multiplier Tests for Fractional Integration," Economics Working Papers 2002-18, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:aarhec:2002-18
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    References listed on IDEAS

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    Cited by:

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    2. 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.
    3. Apergis, Nicholas & Tsoumas, Chris, 2011. "Integration properties of disaggregated solar, geothermal and biomass energy consumption in the U.S," Energy Policy, Elsevier, vol. 39(9), pages 5474-5479, September.
    4. Apergis, Nicholas & Tsoumas, Chris, 2012. "Long memory and disaggregated energy consumption: Evidence from fossils, coal and electricity retail in the U.S," Energy Economics, Elsevier, vol. 34(4), pages 1082-1087.
    5. Katarzyna Łasak & Carlos Velasco, 2015. "Fractional Cointegration Rank Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 241-254, April.
    6. Caporin, Massimiliano & Ranaldo, Angelo & Santucci de Magistris, Paolo, 2013. "On the predictability of stock prices: A case for high and low prices," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5132-5146.
    7. Javier Hualde & Morten {O}rregaard Nielsen, 2022. "Fractional integration and cointegration," Papers 2211.10235, arXiv.org.
    8. 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.
    9. Jorge V Pérez-Rodríguez & María Santana-Gallego, 2020. "Modelling tourism receipts and associated risks, using long-range dependence models," Tourism Economics, , vol. 26(1), pages 70-96, February.
    10. Belbute, José, 2013. "Does final demand for energy in Portugal exhibit long memory?," MPRA Paper 45717, University Library of Munich, Germany.
    11. Gil-Alana, Luis Alberiko & Moreno, Antonio, 2009. "Technology Shocks And Hours Worked: A Fractional Integration Perspective," Macroeconomic Dynamics, Cambridge University Press, vol. 13(5), pages 580-604, November.
    12. 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.
    13. Marina Balboa & Paulo M. M. Rodrigues & Antonio Rubia & A. M. Robert Taylor, 2021. "Multivariate fractional integration tests allowing for conditional heteroskedasticity with an application to return volatility and trading volume," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(5), pages 544-565, August.
    14. P. Sephton, 2008. "Exchange rates and fractional integration revisited," Applied Financial Economics Letters, Taylor and Francis Journals, vol. 4(6), pages 383-387.
    15. 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).
    16. Lean, Hooi Hooi & Smyth, Russell, 2009. "Long memory in US disaggregated petroleum consumption: Evidence from univariate and multivariate LM tests for fractional integration," Energy Policy, Elsevier, vol. 37(8), pages 3205-3211, August.
    17. Fredrik Andersson, 2014. "Exchange rates dynamics revisited: a panel data test of the fractional integration order," Empirical Economics, Springer, vol. 47(2), pages 389-409, September.
    18. Lasak, Katarzyna, 2010. "Likelihood based testing for no fractional cointegration," Journal of Econometrics, Elsevier, vol. 158(1), pages 67-77, September.
    19. 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.
    20. Kassouri, Yacouba, 2022. "Boom-bust cycles in oil consumption: The role of explosive bubbles and asymmetric adjustments," Energy Economics, Elsevier, vol. 111(C).
    21. Gil-Alana, Luis A. & Fischer, Christian, 2007. "International traveling and trade: further evidence for the case of Spanish wine based on fractional VAR specifications," 105th Seminar, March 8-10, 2007, Bologna, Italy 7859, European Association of Agricultural Economists.
    22. Meng, Ming & Payne, James E. & Lee, Junsoo, 2013. "Convergence in per capita energy use among OECD countries," Energy Economics, Elsevier, vol. 36(C), pages 536-545.
    23. Barros, Carlos Pestana & Gil-Alana, Luis A. & Payne, James E., 2013. "U.S. Disaggregated renewable energy consumption: Persistence and long memory behavior," Energy Economics, Elsevier, vol. 40(C), pages 425-432.
    24. Niels Haldrup & Robinson Kruse, 2014. "Discriminating between fractional integration and spurious long memory," CREATES Research Papers 2014-19, Department of Economics and Business Economics, Aarhus University.
    25. Golpe, Antonio A. & Carmona, Monica & Congregado, Emilio, 2012. "Persistence in natural gas consumption in the US: An unobserved component model," Energy Policy, Elsevier, vol. 46(C), pages 594-600.

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    More about this item

    Keywords

    Asymptotic Local Power; Efficient Test; Fractional Integration; Lagrange Multiplier Test; Multivariate Fractional Unit Root; Nonstationarity;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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