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TIME SERIES ANALYSIS

Test for Parameter Change in Linear Processes Based on Whittle's Estimator

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Pages 2129-2141 | Received 11 Feb 2005, Accepted 13 Oct 2006, Published online: 30 Aug 2007

References

  • Bai , J. ( 1994 ). Weak convergence of the sequential empirical processes of residuals in ARMA models . Ann. Statist. 22 : 2051 – 2061 .
  • Basseville , M. , Nikiforov , I. V. ( 1993 ). Detection of Abrupt Changes: Theory and Applications . New Jersey : Prentice Hall .
  • Beran , J. , Terrin , N. ( 1996 ). Testing for a change of the long-memory parameter . Biometrika 83 : 627 – 638 .
  • Beran , J. , Terrin , N. ( 1999 ). Amendments and corrections. “Testing for a change of the long-memory parameter” . Biometrika 86 : 233 .
  • Berkes , I. , Horváth , L. , Kokoszka , P. S. ( 2004 ). Testing for parameter consistancy in Garch(p,q) models . Statist. Probab. Lett. 70 : 263 – 273 .
  • Billingsley , P. ( 1968 ). Convergence of Probability Measures . New York : Wiley .
  • Brockwell , P. J. , Davis , R. A. ( 1990 ). Time Series: Theory and Methods. , 2nd ed. New York : Springer .
  • Brown , R. L. , Durbin , J. , Evans , J. M. ( 1975 ). Techniques for testing the constancy of regression relationships over time . J. Roy. Statist. Soc. Ser. B. 37 : 149 – 163 .
  • Chen , J. , Gupta , A. K. ( 2000 ). Parametric Statistical Change Point Analysis . Boston : Birkäuser .
  • Csörgő , M. , Horváth , L. ( 1997 ). Limit Theorems in Change-point Analysis . New York : Wiley .
  • Deistler , M. , Dunsmuir , W. , Hannan , E. J. ( 1978 ). Vector linear time series models: corrections and extensions . Adv. Appl. Probab. 10 : 360 – 372 .
  • Dunsmuir , W. , Hannan , E. J. ( 1976 ). Vector Linear time series models . Adv. Appl. Probab. 8 : 339 – 364 .
  • Gaenssler , P. , Haeusler , E. ( 1986 ). On martingale central limit theory . In: Eberlein , E. , Taqqu , M. S. , Eds. Dependence in Probability and Statistics . Boston : Birkhäuser , pp. 303 – 334 .
  • Gombay , E. , Horváth , L. ( 1996 ). On the rate of approximations for maximum likelihood tests in change-point models . J. Multivariate Anal. 56 : 120 – 152 .
  • Hamilton , J. D. ( 1994 ). Time Series Analysis . Princeton , New Jersey : Princeton University Press .
  • Hannan , E. J. ( 1973 ). The asymptotic theory of linear time series models . J. Appl. Probab. 10 : 130 – 145 .
  • Horváth , L. ( 2001 ). Change-point detection in long-memory processes . J. Multivariate Anal. 78 : 218 – 234 .
  • Horváth , L. , Shao , Q. ( 1999 ) Limit theorems for quadratic forms with applications to whittle's estimate . Ann. Appl. Probab. 9 : 146 – 187 .
  • Inclán , C. , Tiao , G. C. (1994). Use of cumulative sums of squares for retrospective detection of changes of variances. J. Amer. Statist. Assoc. 89:913–923.
  • Kiefer , J. ( 1959 ). K-sample analogues of the Kolmogorov–Smirnov and Cramer-von Mises tests . Ann. Math. Statist. 30 : 420 – 447 .
  • Lee , S. , Park , S. ( 2001 ). The cusum of squares test for scale changes in infinite order moving average processes . Scand. J. Statist. 28 : 625 – 644 .
  • Lee , S. , Lee , T. ( 2004 ). Cusum test for parameter change based on the maximum likelihood estimator . Sequential Anal. 23 : 239 – 256 .
  • Lee , S. , Na , O. ( 2005 ). Test for parameter change in stochastic processes based on conditional least squares estimator . J. Multivariate Anal. 93 : 375 – 393 .
  • Lee , S. , Ha , J. , Na , O. , Na , S. ( 2003 ). The cusum test for parameter change in time series models . Scand. J. Statist. 30 : 781 – 796 .
  • Lee , S. , Park , S. , Maekawa , K. , Kawai , K. ( 2006 ). Test for parameter change in ARIMA models . Commun. Statist. Theor. Meth. 35 : 429 – 439 .
  • Page , E. S. ( 1955 ). A test for change in a parameter occurring at an unknown point . Biometrika 42 : 523 – 527 .
  • Phillips , P. C. , Solo , V. ( 1992 ). Asymptotics for linear processes . Ann. Statist. 20 : 971 – 1001 .
  • Picard , D. ( 1985 ). Testing and estimating change-points in time series . Adv. Appl. Probab. 17 : 841 – 867 .
  • Rosenblatt , M. ( 1985 ). Stationary Sequences and Random Fields . New York : Birkhäuser .
  • Walker , A. M. ( 1964 ). Asymptotic properties of least-square estimates of parameters of the spectrum of a stationary nondeterministic time series . J. Austral. Math. Soc. 4 : 363 – 384 .
  • Whittle , P. ( 1952 ). Some results in time seried analysis . Skandivanisk Aktuarietidskrift. 35 : 48 – 60 .
  • Whittle , P. ( 1962 ). Gaussian estimation in stationary time series . Bull. Instit. Internet. Statist. 39–2 : 105 – 129 .

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