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Asymptotic Behavior Of The Cusum Of Squares Test Under Stochastic And Deterministic Time Trends

  • Nielsen, Bent
  • Sohkanen, Jouni S.

We generalize the cumulative sum of squares (CUSQ) test to the case of nonstationary autoregressive distributed lag models with deterministic time trends. The test may be implemented with either ordinary least squares residuals or standardized forecast errors. In explosive cases the asymptotic theory applies more generally for the least squares residuals-based test. Preliminary simulations of the tests suggest a very modest difference between the tests and a very modest variation with nuisance parameters. This supports the use of the tests in explorative analysis.

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

Volume (Year): 27 (2011)
Issue (Month): 04 (August)
Pages: 913-927

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Handle: RePEc:cup:etheor:v:27:y:2011:i:04:p:913-927_00
Contact details of provider: Postal: Cambridge University Press, UPH, Shaftesbury Road, Cambridge CB2 8BS UK
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  1. Deng, Ai & Perron, Pierre, 2008. "The Limit Distribution Of The Cusum Of Squares Test Under General Mixing Conditions," Econometric Theory, Cambridge University Press, vol. 24(03), pages 809-822, June.
  2. Lu, Xinhong & Maekawa, Koichi & Lee, Sangyeol, 2008. "The CUSUM of squares test for the stability of regression models with non-stationary regressors," Economics Letters, Elsevier, vol. 100(2), pages 234-237, August.
  3. Margaret M. McConnell & Gabriel Perez Quiros, 1997. "Output fluctuations in the United States: what has changed since the early 1980s?," Research Paper 9735, Federal Reserve Bank of New York.
  4. Bent Nielsen, 2003. "Strong consistency results for least squares estimators in general vector autoregressions with deterministic terms," Economics Papers 2003-W23, Economics Group, Nuffield College, University of Oxford.
  5. Ploberger, Werner & Kramer, Walter, 1986. "On studentizing a test for structural change," Economics Letters, Elsevier, vol. 20(4), pages 341-344.
  6. Ai Deng & Pierre Perron, 2005. "A Non-local Perspective on the Power Properties of the CUSUM and CUSUM of Squares Tests for Structural Change," Boston University - Department of Economics - Working Papers Series WP2005-047, Boston University - Department of Economics.
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