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Multivariate Lagrange Multiplier Tests for Fractional Integration

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  • Morten Ørregaard Nielsen

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 noncentral 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 and 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 variable is also introduced. The finite sample properties of the LM test are evaluated by Monte Carlo experiments which demonstrate that it is superior to the Breitung and Hassler (2002) test. 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. Copyright 2005, Oxford University Press.

Suggested Citation

  • Morten Ørregaard Nielsen, 2005. "Multivariate Lagrange Multiplier Tests for Fractional Integration," Journal of Financial Econometrics, Oxford University Press, vol. 3(3), pages 372-398.
    • Handle: RePEc:oup:jfinec:v:3:y:2005:i:3:p:372-398
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbi017
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Belbute, José, 2013. "Does final demand for energy in Portugal exhibit long memory?," MPRA Paper 45717, University Library of Munich, Germany.
    5. 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.
    6. Smyth, Russell, 2013. "Are fluctuations in energy variables permanent or transitory? A survey of the literature on the integration properties of energy consumption and production," Applied Energy, Elsevier, vol. 104(C), pages 371-378.
    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. Katarzyna Łasak & Carlos Velasco, 2015. "Fractional Cointegration Rank Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 241-254, April.
    10. 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.
    11. Lasak, Katarzyna, 2010. "Likelihood based testing for no fractional cointegration," Journal of Econometrics, Elsevier, vol. 158(1), pages 67-77, September.
    12. 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.
    13. 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.
    14. 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).
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    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. 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.
    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. 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.
    24. 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.

    More about this item

    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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