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Subsampling tests for variance changes in the presence of autoregressive parameter shifts

  • Jin, Hao
  • Zhang, Jinsuo
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    In this paper, we consider the problem of testing for variance changes in the linear autoregressive processes including AR(p) processes when there are autoregressive parameter shifts. In performing a test, we employ the conventional residual CUSUM of squares test (RCUSQ) statistic. The RCUSQ test is based on the subsampling method introduced by Jach and Kokoszka (2004) [16] to eliminate the influence caused by autoregressive parameter shifts. It is shown that under regularity conditions, the test statistic behaves asymptotically the function of a standard Brownian bridge. We establish the asymptotic validity of this method and assess its performance both theoretically and numerically.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 101 (2010)
    Issue (Month): 10 (November)
    Pages: 2255-2265

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    Handle: RePEc:eee:jmvana:v:101:y:2010:i:10:p:2255-2265
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    1. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
    2. Jin, Hao & Tian, Zheng & Qin, Ruibing, 2009. "Bootstrap tests for structural change with infinite variance observations," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 1985-1995, October.
    3. Last, Michael & Shumway, Robert, 2008. "Detecting abrupt changes in a piecewise locally stationary time series," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 191-214, February.
    4. Kokoszka, Piotr & Leipus, Remigijus, 1998. "Change-point in the mean of dependent observations," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 385-393, November.
    5. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    6. Perron, P., 1989. "Testing For A Unit Root In A Time Series With A Changing Mean," Papers 347, Princeton, Department of Economics - Econometric Research Program.
    7. 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.
    8. Bhattacharya, P.K., 1987. "Maximum likelihood estimation of a change-point in the distribution of independent random variables: General multiparameter case," Journal of Multivariate Analysis, Elsevier, vol. 23(2), pages 183-208, December.
    9. Gombay, Edit, 2008. "Change detection in autoregressive time series," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 451-464, March.
    10. Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 551-563, November.
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