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Distribution Approximations for Cusum and Cusumsq Statistics

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  • Reza Habibi

Abstract

The cumulative sum (cusum) is an important statistics in testing for a change point. This paper is concerned with the distribution approximations to the cusum statistic under the null and alternative hypotheses. We also consider distribution approximations for the cumulative sum of squares (cusumsq) test statistics. Finally, a discussion section is given.

Suggested Citation

  • Reza Habibi, 2010. "Distribution Approximations for Cusum and Cusumsq Statistics," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 11(3), pages 585-596, December.
    • Handle: RePEc:csb:stintr:v:11:y:2010:i:3:p:585-596
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    References listed on IDEAS

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    1. Halunga, Andreea G. & Osborn, Denise R. & Sensier, Marianne, 2009. "Changes in the order of integration of US and UK inflation," Economics Letters, Elsevier, vol. 102(1), pages 30-32, January.
    2. Eric Hillebrand & Gunther Schnabl, 2003. "The Effects of Japanese Foreign Exchange Intervention: GARCH Estimation and Change Point Detection," Departmental Working Papers 2003-09, Department of Economics, Louisiana State University.
    3. Andreu Sansó & Vicent Aragó & Josep Lluís Carrion, 2003. "Testing for Changes in the Unconditional Variance of Financial Time Series," DEA Working Papers 5, Universitat de les Illes Balears, Departament d'Economía Aplicada.
    4. Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, vol. 60(2), pages 271-285, March.
    5. Denis Conniffe & John E. Spencer, 1999. "Approximating the Distribution of the Maximum Partial Sum of Normal Deviates," Papers WP102, Economic and Social Research Institute (ESRI).
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