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A Joint Chow Test for Structural Instability

  • Bent Nielsen
  • Andrew Whitby

The classical Chow (1960) test for structural instability requires strictly exogenous regressors and a break-point specified in advance.� In this paper we consider two generalisations, the 1-step recursive Chow test (based on the sequence of studentized recursive residuals) and its supremum counterpart, which relax these requirements.� We use results on strong consistency of regression estimators to show that the 1-step test is appropriate for stationary, unit root or explosive processes modelled in the autoregressive distributed lags (ADL) framework.� We then use results in extreme value theory to develop a new supremum version of the test, suitable for formal testing of structural instability with an unknown break-point.� The test assumes normality of errors, and is intended to be used in situations where this can either be assumed or established empirically.

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Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 2012-W07.

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Date of creation: 25 Jun 2012
Date of revision:
Handle: RePEc:oxf:wpaper:2012-w07
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  1. Hendry, David F, 1986. "Using PC-GIVE in Econometrics Teaching," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(1), pages 87-98, February.
  2. 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.
  3. Jouni Sohkanen & B. Nielsen, 2009. "Asymptotic behaviour of the CUSUM of squares test under stochastic and deterministic time trends," Economics Papers 2009-W09, Economics Group, Nuffield College, University of Oxford.
  4. Johansen, S., 1999. "A Bartlett Correction Factor for Tests on the Cointegrating Relations," Economics Working Papers eco99/10, European University Institute.
  5. Bengt Assarsson & Claes Berg & Per Jansson, 2004. "Investment in Swedish manufacturing: Analysis and forecasts," Empirical Economics, Springer, vol. 29(2), pages 261-280, 05.
  6. Dufour, Jean-Marie, 1982. "Recursive stability analysis of linear regression relationships: An exploratory methodology," Journal of Econometrics, Elsevier, vol. 19(1), pages 31-76, May.
  7. Ploberger, Werner & Kramer, Walter, 1986. "On studentizing a test for structural change," Economics Letters, Elsevier, vol. 20(4), pages 341-344.
  8. James H. Stock & Mark W. Watson, 2002. "Has the Business Cycle Changed and Why?," NBER Working Papers 9127, National Bureau of Economic Research, Inc.
  9. Bauer, Dietmar, 2009. "Almost Sure Bounds On The Estimation Error For Ols Estimators When The Regressors Include Certain Mfi(1) Processes," Econometric Theory, Cambridge University Press, vol. 25(02), pages 571-582, April.
  10. Eric Engler & Bent Nielsen, 2007. "The empirical process of autoregressive residuals," Economics Series Working Papers 2007-W01, University of Oxford, Department of Economics.
  11. Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation for Research in Economics, Yale University.
  12. Kilian, Lutz & Demiroglu, Ufuk, 2000. "Residual-Based Tests for Normality in Autoregressions: Asymptotic Theory and Simulation Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 40-50, January.
  13. Peter Burridge & A. M. Robert Taylor, 2006. "Additive Outlier Detection Via Extreme-Value Theory," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(5), pages 685-701, 09.
  14. Hendry, David F., 1995. "Dynamic Econometrics," OUP Catalogue, Oxford University Press, number 9780198283164, July.
  15. Kramer, Walter & Ploberger, Werner & Alt, Raimund, 1988. "Testing for Structural Change in Dynamic Models," Econometrica, Econometric Society, vol. 56(6), pages 1355-69, November.
  16. Jurgen A. Doornik & Henrik Hansen, 2008. "An Omnibus Test for Univariate and Multivariate Normality," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 927-939, December.
  17. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037, July.
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