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Multivariate Lagrange Multiplier Tests for Fractional Integration

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  • Morten �rregaard 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.

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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. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 15(04), pages 549-582, August.
  2. Breitung, Jorg & Hassler, Uwe, 2002. "Inference on the cointegration rank in fractionally integrated processes," Journal of Econometrics, Elsevier, Elsevier, vol. 110(2), pages 167-185, October.
  3. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, Elsevier, vol. 47(1), pages 67-84, January.
  4. Kugler, Peter & Neusser, K, 1993. "International Real Interest Rate Equalization: A Multivariate Time-Series Approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 8(2), pages 163-74, April-Jun.
  5. Phillips, P C B & Durlauf, S N, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 53(4), pages 473-95, August.
  6. Nyblom, Jukka & Harvey, Andrew, 2000. "Tests Of Common Stochastic Trends," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 16(02), pages 176-199, April.
  7. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 12(2-3), pages 231-254.
  8. Choi, In & Chul Ahn, Byung, 1998. "Testing the null of stationarity for multiple time series," Journal of Econometrics, Elsevier, Elsevier, vol. 88(1), pages 41-77, November.
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Cited by:
  1. 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, Elsevier, vol. 40(C), pages 425-432.
  2. 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, Elsevier, vol. 37(8), pages 3205-3211, August.
  3. 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," Development Research Unit Working Paper Series, Monash University, Department of Economics 04-12, Monash University, Department of Economics.
  4. Katarzyna Lasak & Carlos Velasco, 2013. "Fractional cointegration rank estimation," CREATES Research Papers, School of Economics and Management, University of Aarhus 2013-08, School of Economics and Management, University of Aarhus.
  5. Lasak, Katarzyna, 2010. "Likelihood based testing for no fractional cointegration," Journal of Econometrics, Elsevier, Elsevier, vol. 158(1), pages 67-77, September.
  6. 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, Elsevier, vol. 76(C), pages 502-522.
  7. Niels Haldrup & Robinson Kruse, 2014. "Discriminating between fractional integration and spurious long memory," CREATES Research Papers, School of Economics and Management, University of Aarhus 2014-19, School of Economics and Management, University of Aarhus.
  8. Massimiliano Caporin & Angelo Ranaldo, 2011. "On the Predictability of Stock Prices: a Case for High and Low Prices," Working Papers, Swiss National Bank 2011-11, Swiss National Bank.
  9. Avarucci, Marco & Velasco, Carlos, 2008. "A Wald Test for the Cointegration Rank in Nonstationary Fractional Systems," Research Memorandum, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) 049, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  10. Uwe Hassler & Matei Demetrescu & Adina Tarcolea, 2011. "Asymptotic normal tests for integration in panels with cross-dependent units," AStA Advances in Statistical Analysis, Springer, Springer, vol. 95(2), pages 187-204, June.
  11. Belbute, José, 2013. "Does final demand for energy in Portugal exhibit long memory?," MPRA Paper 45717, University Library of Munich, Germany.
  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, European Association of Agricultural Economists 7859, European Association of Agricultural Economists.
  13. 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, Elsevier, vol. 34(4), pages 1082-1087.
  14. Gil-Alana, Luis Alberiko & Moreno, Antonio, 2009. "Technology Shocks And Hours Worked: A Fractional Integration Perspective," Macroeconomic Dynamics, Cambridge University Press, Cambridge University Press, vol. 13(05), pages 580-604, November.
  15. Apergis, Nicholas & Tsoumas, Chris, 2011. "Integration properties of disaggregated solar, geothermal and biomass energy consumption in the U.S," Energy Policy, Elsevier, Elsevier, vol. 39(9), pages 5474-5479, September.

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