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A Residual-Based Lm-Type Test Against Fractional Cointegration

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  • Hassler, Uwe
  • Breitung, J rg

Abstract

Nonstationary integrated time series may be fractionally cointegrated. Here we propose a test for the null hypothesis of no cointegration. It builds on the asymptotically normal Lagrange multiplier (LM) test against fractional alternatives applied to single equation residuals. It is shown that the LM test applied naively to residuals from a static level regression does not retain asymptotic normality. However, when the LM statistic is employed with residuals from a regression of differenced variables, then the test statistic is shown to have a standard normal limiting distribution. Monte Carlo experiments establish its relevance in finite samples.We thank Norbert Christopeit and three anonymous referees for corrections and very valuable comments.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 22 (2006)
Issue (Month): 06 (December)
Pages: 1091-1111

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Handle: RePEc:cup:etheor:v:22:y:2006:i:06:p:1091-1111_06

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Cited by:
  1. Uwe Hassler & Paulo M.M. Rodrigues & Antonio Rubia, 2012. "Quantile regression for long memory testing: A case of realized volatility," Working Papers w201207, Banco de Portugal, Economics and Research Department.
  2. Katsumi Shimotsu & Morten Ørregaard Nielsen, 2006. "Determining the Cointegrating Rank in Nonstationary Fractional Systems by the Exact Local Whittle Approach," Working Papers 1029, Queen's University, Department of Economics.
  3. Avarucci, Marco & Velasco, Carlos, 2008. "A Wald Test for the Cointegration Rank in Nonstationary Fractional Systems," Research Memorandum 049, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  4. 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.
  5. Katarzyna Lasak, 2008. "Likelihood based testing for no fractional cointegration," CREATES Research Papers 2008-52, School of Economics and Management, University of Aarhus.
  6. Hassler, Uwe & Meller, Barbara, 2011. "Detecting multiple breaks in long memory: The case of US inflation," Discussion Paper Series 1: Economic Studies 2011,26, Deutsche Bundesbank, Research Centre.
  7. 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.

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