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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.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series Economics Working Papers with number 2002-18.

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Handle: RePEc:aah:aarhec:2002-18

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Asymptotic Local Power; Efficient Test; Fractional Integration; Lagrange Multiplier Test; Multivariate Fractional Unit Root; Nonstationarity;

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References

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  1. Peter KUGLER & Klaus NEUSSER, 1990. "International Real Interest Rate Equalization: A Multivariate Time Series Approach," Vienna Economics Papers vie9003, University of Vienna, Department of Economics.
  2. Phillips, P C B & Durlauf, S N, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Wiley Blackwell, vol. 53(4), pages 473-95, August.
  3. Choi, In & Chul Ahn, Byung, 1998. "Testing the null of stationarity for multiple time series," Journal of Econometrics, Elsevier, vol. 88(1), pages 41-77, November.
  4. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August.
  5. Breitung, Jorg & Hassler, Uwe, 2002. "Inference on the cointegration rank in fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 110(2), pages 167-185, October.
  6. Nyblom, Jukka & Harvey, Andrew, 1999. "Tests of Common Stochastic Trends," Cambridge Working Papers in Economics 9902, Faculty of Economics, University of Cambridge.
  7. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
  8. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
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Cited by:
  1. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2006. "Fractional Integration And Impulse Responses: A Bivariate Application To Real Output In The Us And The Scandinavian Countries," Economics and Finance Discussion Papers 06-25, Economics and Finance Section, School of Social Sciences, Brunel University.
  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. Katarzyna Lasak & Carlos Velasco, 2013. "Fractional cointegration rank estimation," CREATES Research Papers 2013-08, School of Economics and Management, University of Aarhus.
  5. Massimiliano Caporin & Angelo Ranaldo & Paolo Santucci de Magistris, 2011. "On the Predictability of Stock Prices: A Case for High and Low Prices," "Marco Fanno" Working Papers 0136, Dipartimento di Scienze Economiche "Marco Fanno".
  6. Gil-Alana, Luis Alberiko & Moreno, Antonio, 2009. "Technology Shocks And Hours Worked: A Fractional Integration Perspective," Macroeconomic Dynamics, Cambridge University Press, vol. 13(05), pages 580-604, November.
  7. Uwe Hassler & Matei Demetrescu & Adina Tarcolea, 2011. "Asymptotic normal tests for integration in panels with cross-dependent units," AStA Advances in Statistical Analysis, Springer, vol. 95(2), pages 187-204, June.
  8. 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.
  9. Katarzyna Lasak, 2008. "Likelihood based testing for no fractional cointegration," CREATES Research Papers 2008-52, School of Economics and Management, University of Aarhus.
  10. Luis F. Martins & Paulo M.M. Rodrigues, 2010. "Testing for Persistence Change in Fractionally Integrated Models: An Application to World Inflation Rates," Working Papers w201030, Banco de Portugal, Economics and Research Department.
  11. Russell Smyth, 2012. "Are fluctuations in energy variables permanent or transitory? A survey of the literature on the integration properties of energy consumption and production," Monash Economics Working Papers 04-12, Monash University, Department of Economics.
  12. 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.

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