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The Limit Distribution of the CUSUM of Squares Test Under General Mixing Conditions

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Author Info

  • Ai Deng

    ()
    (Bates White, LLC)

  • Pierre Perron

    ()
    (Department of Economics, Boston University)

Abstract

We consider the CUSUM of squares test in a linear regression model with general mixing assumptions on the regressors and the errors. We derive its limit distribution and show how it depends on the nature of the error process. We suggest a corrected version that has a limit distribution free of nuisance parameters. We also discuss how it provides an improvement over the standard approach to testing for a change in the variance in a univariate times series. Simulation evidence is presented to support this.

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File URL: http://people.bu.edu/perron/papers/cus-lim.pdf
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Bibliographic Info

Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number wp2006-004.

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Length: 13 pages
Date of creation: Nov 2006
Date of revision:
Handle: RePEc:bos:wpaper:wp2006-004

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Related research

Keywords: Change-point; Variance shift; Recursive residuals; Dynamic models; Conditional heteroskedasticity.;

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References

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  1. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  2. Ploberger, Werner & Krämer;, Walter, 1990. "The Local Power of the CUSUM and CUSUM of Squares Tests," Econometric Theory, Cambridge University Press, vol. 6(03), pages 335-347, September.
  3. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
  4. Ploberger, Werner & Kramer, Walter, 1986. "On studentizing a test for structural change," Economics Letters, Elsevier, vol. 20(4), pages 341-344.
  5. James H. Stock & Mark W. Watson, 2002. "Has the Business Cycle Changed and Why?," NBER Working Papers 9127, National Bureau of Economic Research, Inc.
  6. Pagan, Adrian R. & Schwert, G. William, 1990. "Testing for covariance stationarity in stock market data," Economics Letters, Elsevier, vol. 33(2), pages 165-170, June.
  7. Donald W.K. Andrews & Christopher J. Monahan, 1990. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Cowles Foundation Discussion Papers 942, Cowles Foundation for Research in Economics, Yale University.
  8. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2007. "Testing for unit roots in time series models with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 140(2), pages 919-947, October.
  9. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  10. 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.
  11. Sangyeol Lee & Jeongcheol Ha & Okyoung Na & Seongryong Na, 2003. "The Cusum Test for Parameter Change in Time Series Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 30(4), pages 781-796.
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Citations

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Cited by:
  1. Pierre Perron & Jing Zhou, 2008. "Testing Jointly for Structural Changes in the Error Variance and Coefficients of a Linear Regression Model," Boston University - Department of Economics - Working Papers Series wp2008-011, Boston University - Department of Economics.
  2. 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.
  3. Pierre Perron & Tatsushi Oka, 2011. "Testing for Common Breaks in a Multiple Equations System," Boston University - Department of Economics - Working Papers Series WP2011-057, Boston University - Department of Economics.
  4. Xu, Ke-Li, 2013. "Power monotonicity in detecting volatility levels change," Economics Letters, Elsevier, vol. 121(1), pages 64-69.
  5. Pierre Perron & Tomoyoshi Yabu, . "Estimating Deterministic Trends with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series WP2006-012, Boston University - Department of Economics, revised Feb 2006.
  6. Loredana Ureche-Rangau & Franck Speeg, 2011. "A simple method for variance shift detection at unknown time points," Economics Bulletin, AccessEcon, vol. 31(3), pages 2204-2218.
  7. Sahbi FARHANI, 2012. "Tests of Parameters Instability: Theoretical Study and Empirical Analysis on Two Types of Models (ARMA Model and Market Model)," International Journal of Economics and Financial Issues, Econjournals, vol. 2(3), pages 246-266.
  8. Jing Zhou & Pierre Perron, 2008. "Testing for Breaks in Coefficients and Error Variance: Simulations and Applications," Boston University - Department of Economics - Working Papers Series wp2008-010, Boston University - Department of Economics.
  9. Xu, Ke-Li, 2013. "Powerful tests for structural changes in volatility," Journal of Econometrics, Elsevier, vol. 173(1), pages 126-142.
  10. 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.
  11. Paulo M.M. Rodrigues & Antonio Rubia, 2010. "The Effects of Additive Outliers and Measurement Errors when Testing for Structural Breaks in Variance," Working Papers w201011, Banco de Portugal, Economics and Research Department.
  12. Hsu, Chih-Chiang, 2007. "The MOSUM of squares test for monitoring variance changes," Finance Research Letters, Elsevier, vol. 4(4), pages 254-260, December.
  13. Stanislav Anatolyev & Grigory Kosenok, 2011. "Sequential Testing with Uniformly Distributed Size," Working Papers w0123, Center for Economic and Financial Research (CEFIR).
  14. Sensoy, Ahmet, 2013. "Dynamic relationship between precious metals," Resources Policy, Elsevier, vol. 38(4), pages 504-511.
  15. Xu, Ke-Li, 2008. "Testing against nonstationary volatility in time series," Economics Letters, Elsevier, vol. 101(3), pages 288-292, December.

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