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Sequential Testing with Uniformly Distributed Size

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  • Stanislav Anatolyev

    ()
    (New Economic School)

  • Grigory Kosenok

    (New Economic School)

Abstract

Sequential procedures of testing for structural stability do not provide enough guidance on the shape of boundaries that are used to decide on acceptance or rejection, requiring only that the overall size of the test is asymptotically controlled. We introduce and motivate a reasonable criterion for a shape of boundaries which requires that the test size be uniformly distributed over the testing period. Under this criterion, we numerically construct boundaries for most popular sequential tests that are characterized by a test statistic behaving asymptotically either as a Wiener process or Brownian bridge. We handle this problem both in a context of retrospecting a historical sample and in a context of monitoring newly arriving data. We tabulate the boundaries by tting them to certain ‡exible but parsimonious functional forms. Interesting patterns emerge in an illustrative application of sequential tests to the Phillips curve model.

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Bibliographic Info

Paper provided by Center for Economic and Financial Research (CEFIR) in its series Working Papers with number w0123.

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Length: 43 pages
Date of creation: Apr 2011
Date of revision:
Handle: RePEc:cfr:cefirw:w0123

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Related research

Keywords: Structural stability; sequential tests; CUSUM; retrospection; monitoring; boundaries; asymptotic size;

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References

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  1. Chu, Chia-Shang James & Hornik, Kurt & Kuan, Chung-Ming, 1995. "The Moving-Estimates Test for Parameter Stability," Econometric Theory, Cambridge University Press, vol. 11(04), pages 699-720, August.
  2. 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.
  3. Ploberger, Werner & Kramer, Walter & Kontrus, Karl, 1989. "A new test for structural stability in the linear regression model," Journal of Econometrics, Elsevier, vol. 40(2), pages 307-318, February.
  4. Elena Andreou & Eric Ghysels, 2001. "Detecting Mutiple Breaks in Financial Market Volatility Dynamics," CIRANO Working Papers 2001s-65, CIRANO.
  5. 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.
  6. Ghysels, E. & Guay, A. & Hall, A., 1995. "Predictive Tests for Structural Change with Unknown Breakpoint," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 9524, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  7. Kramer, Walter & Ploberger, Werner & Alt, Raimund, 1988. "Testing for Structural Change in Dynamic Models," Econometrica, Econometric Society, Econometric Society, vol. 56(6), pages 1355-69, November.
  8. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 9552, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  9. Inoue, Atsushi & Rossi, Barbara, 2005. "Recursive Predictability Tests for Real-Time Data," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 23, pages 336-345, July.
  10. Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, Econometric Society, vol. 60(2), pages 271-85, March.
  11. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
  12. Andreou, Elena & Ghysels, Eric, 2006. "Monitoring disruptions in financial markets," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 77-124.
  13. Kurt Hornik & Friedrich Leisch & Christian Kleiber & Achim Zeileis, 2005. "Monitoring structural change in dynamic econometric models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 20(1), pages 99-121.
  14. Chu, Chia-Shang James & Stinchcombe, Maxwell & White, Halbert, 1996. "Monitoring Structural Change," Econometrica, Econometric Society, Econometric Society, vol. 64(5), pages 1045-65, September.
  15. Leisch, Friedrich & Hornik, Kurt & Kuan, Chung-Ming, 2000. "Monitoring Structural Changes With The Generalized Fluctuation Test," Econometric Theory, Cambridge University Press, vol. 16(06), pages 835-854, December.
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