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The Limit Distribution Of The Cusum Of Squares Test Under General Mixing Conditions

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  • Deng, Ai
  • Perron, Pierre

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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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 24 (2008)
Issue (Month): 03 (June)
Pages: 809-822

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Handle: RePEc:cup:etheor:v:24:y:2008:i:03:p:809-822_08

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  1. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
  2. 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.
  3. Ploberger, Werner & Kramer, Walter, 1986. "On studentizing a test for structural change," Economics Letters, Elsevier, vol. 20(4), pages 341-344.
  4. 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.
  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. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-66, July.
  7. 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.
  8. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  9. 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.
  10. 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.
  11. repec:att:wimass:9208 is not listed on IDEAS
  12. Loretan, Mico & Phillips, Peter C. B., 1994. "Testing the covariance stationarity of heavy-tailed time series: An overview of the theory with applications to several financial datasets," Journal of Empirical Finance, Elsevier, vol. 1(2), pages 211-248, January.
  13. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
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Cited by:
  1. Paulo M. M. Rodrigues & Antonio Rubia, 2011. "The Effects of Additive Outliers and Measurement Errors when Testing for Structural Breaks in Variance," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 73(4), pages 449-468, 08.
  2. Xu, Ke-Li, 2008. "Testing against nonstationary volatility in time series," Economics Letters, Elsevier, vol. 101(3), pages 288-292, December.
  3. 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.
  4. Deng, Ai & Perron, Pierre, 2008. "A non-local perspective on the power properties of the CUSUM and CUSUM of squares tests for structural change," Journal of Econometrics, Elsevier, vol. 142(1), pages 212-240, January.
  5. Xu, Ke-Li, 2013. "Power monotonicity in detecting volatility levels change," Economics Letters, Elsevier, vol. 121(1), pages 64-69.
  6. Pierre Perron & Tomoyoshi Yabu, 2005. "Estimating Deterministric Trends with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series WP2005-037, Boston University - Department of Economics.
  7. Hsu, Chih-Chiang, 2007. "The MOSUM of squares test for monitoring variance changes," Finance Research Letters, Elsevier, vol. 4(4), pages 254-260, December.
  8. 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.
  9. Bent Nielsen & Jouni Sohkanen, 2009. "Asymptotic behaviour of the CUSUM of squares test under stochastic and deterministic time trends," Economics Series Working Papers 2009-W09, University of Oxford, Department of Economics.
  10. Xu, Ke-Li, 2013. "Powerful tests for structural changes in volatility," Journal of Econometrics, Elsevier, vol. 173(1), pages 126-142.
  11. Sensoy, Ahmet, 2013. "Dynamic relationship between precious metals," Resources Policy, Elsevier, vol. 38(4), pages 504-511.
  12. Stanislav Anatolyev & Grigory Kosenok, 2011. "Sequential Testing with Uniformly Distributed Size," Working Papers w0123, Center for Economic and Financial Research (CEFIR).
  13. 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.
  14. 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.
  15. 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.

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