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Detection of Changes in Linear Sequences

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Abstract

We discuss the asymptotic properties of some tests to detect possible changes in the mean of linear processes.

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References

  • Bai, J. (1994). Least squares estimation of a shift in linear processes, J. Time Ser. Anal., 15, 453–472.

    Google Scholar 

  • Csörgő, M. and Horváth, L. (1988). Nonparametric methods for change-point problems, Handbook of Statistics, 7, 275–280.

    Google Scholar 

  • Csörgő, M. and Horváth, L. (1993). Weighted Approximations in Probability and Statistics, Wiley, New York.

    Google Scholar 

  • Csörgő, M. and Révész, P. (1981). Strong Approximations in Probability and Statistics, Academic Press, New York.

    Google Scholar 

  • Darling, D. A. and Erdős, P. (1956). A limit theorem for maximum of normalized sums of independent random variables, Duke Math. J., 23, 143–155.

    Google Scholar 

  • Davis, R. A., Huang, D. and Yao, Y. C. (1995). Testing for a change in the parameter values and order of an autoregressive model, Ann. Statist., 23, 283–304.

    Google Scholar 

  • Giraitis, L. and Leipus, R. (1990). A functional CLT for nonparametric estimates of spectra and change-point problem for spectral function, Lietuvos Matematikos Rinkinys, 30, 674–697.

    Google Scholar 

  • Giraitis, L. and Leipus, R. (1992). Testing and estimating in the change-point problem of the spectral function, Lietuvos Matematikos Rinkinys, 32, 20–38.

    Google Scholar 

  • Gombay, E. and Horváth, L. (1990). Asymptotic distributions of maximum likelihood tests for change in the mean, Biometrika, 77, 411–414.

    Google Scholar 

  • Gombay, E. and Horváth, L. (1994). An application of the maximum likelihood test to the change-point problem, Stochastic Process. Appl., 50, 161–171.

    Google Scholar 

  • Gorodetskii, V. V. (1977). On the strong mixing property for linear sequences, Theory Probab. Appl., 22, 411–413.

    Google Scholar 

  • Haccou, P., Meelis, E. and Van de Geer, S. (1988). The likelihood ratio test for the change point problem for exponentially distributed random variables, Stochastic Process. Appl., 27, 121–139.

    Google Scholar 

  • Horváth, L. (1993a). Change in autoregressive processes, Stochastic Process. Appl., 44, 221–242.

    Google Scholar 

  • Horváth, L. (1993b). The maximum likelihood method for testing changes in the parameters of normal observations, Ann. Statist., 21, 671–680.

    Google Scholar 

  • Horváth, L. and Kokoszka, P. (1995). The effect of long-range dependence on change-point estimators (preprint).

  • Ibragimov, I. A. and Linnik, Y. V. (1971). Independent and Stationary Sequences of Random Variables, Wolters-Noordhoff, Groningen.

    Google Scholar 

  • Kuelbs, J. and Philipp, W. (1980). Almost sure invariance principles for partial sums of mixing B-valued random variables, Ann. Probab., 8, 1003–1036.

    Google Scholar 

  • Kulpelger, R. J. (1985). On the residuals of autoregressive processes and polynomial regression, Stochastic Process. Appl., 21, 107–118.

    Google Scholar 

  • Page, E. S. (1954). Continuous inspection schemes, Biometrika, 41, 100–105.

    Google Scholar 

  • Page, E. S. (1955). A test for change in a parameter occurring at an unknown point, Biometrika, 42, 523–526.

    Google Scholar 

  • Philipp, W. and Stout, W. (1975). Almost sure invariance principles for partial sums of weakly dependent random variables, Mem. Amer. Math. Soc., 161, 1–137.

    Google Scholar 

  • Picard, D. (1985). Testing and estimating change-points in time series, Adv. in Appl. Probab., 17, 841–867.

    Google Scholar 

  • Sen, A. and Srivastava, M. S. (1975a). On tests for detecting change in the mean, Ann. Statist., 3, 98–108.

    Google Scholar 

  • Son, A. and Srivastava, M. S. (1975b). Some one-sided tests for change in level, Technometrics, 17, 61–64.

    Google Scholar 

  • Shorack, G. R. and Wellner, J. A. (1986). Empirical Processes with Applications to Statistics, Wiley, New York.

    Google Scholar 

  • Tang, S. M. and MacNeill, I. B. (1993). The effect of serial correlation on tests for parameter change at unknown time, Ann. Statist., 21, 552–575.

    Google Scholar 

  • Withers, C. S. (1981). Conditions for linear processes to be strong-mixing, Zeit. Wahrscheinlichkeitsth., 57, 477–480.

    Google Scholar 

  • Worsley, K. J. (1979). On the likelihood ratio test for a shift in location of normal populations, J. Amer. Statist. Assoc., 74, 365–367.

    Google Scholar 

  • Worsley, K. J. (1986). Confidence regions and tests for a change-point in a sequence of exponential random variables, Biometrika, 73, 91–104.

    Google Scholar 

  • Yao, Y. C. and Davis, R. A. (1986). The asymptotic behavior of the likelihood ratio statistic for testing a shift in mean in a sequence of independent normal variates, Sankhyā Ser. A, 48, 339–353.

    Google Scholar 

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Horváth, L. Detection of Changes in Linear Sequences. Annals of the Institute of Statistical Mathematics 49, 271–283 (1997). https://doi.org/10.1023/A:1003110912735

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  • DOI: https://doi.org/10.1023/A:1003110912735

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