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Multivariate Lagrange Multiplier Tests for Fractional Integration

  • Morten �rregaard Nielsen

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.

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File URL: http://hdl.handle.net/10.1093/jjfinec/nbi017
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Article provided by Society for Financial Econometrics in its journal Journal of Financial Econometrics.

Volume (Year): 3 (2005)
Issue (Month): 3 ()
Pages: 372-398

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Handle: RePEc:oup:jfinec:v:3:y:2005:i:3:p:372-398
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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. Nyblom, Jukka & Harvey, Andrew, 2000. "Tests Of Common Stochastic Trends," Econometric Theory, Cambridge University Press, vol. 16(02), pages 176-199, April.
  3. Peter C.B. Phillips & Steven N. Durlauf, 1985. "Multiple Time Series Regression with Integrated Processes," Cowles Foundation Discussion Papers 768, Cowles Foundation for Research in Economics, Yale University.
  4. 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.
  5. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August.
  6. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  7. 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.
  8. 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.
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