Abstract
In this paper we investigate the asymptotic properties of the test statistics for detecting change-points in the variance of infinite moving average sequences with long memory.
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References
Avram F, Taqqu MS (1987) Noncentral limit theorems and Appell polynomials. Ann. Probab. 15, 767–775
Beran J (1992) Statistical methods for data with long-range dependence. Statist. Sci. 7, 404–427
Beran J (1994) Statistics for Long-Memory Processes. Chapman and Hall, New York
Burke MD, Csörgő M, Csörgő S, Révész P (1979) Approximations of the empirical process when parameters are estimated. Ann. Prob. 7, 790–810
Csörgő M, Horváth L (1988) Invariance principles for change-point problems. J. Multivariate Anal. 27, 151–168
Csörgő M, Horváth L (1993) Weighted Approximations in Probability and Statistics. Wiley, Chichester
Csörgő M, Horváth L (1997) Limit Theorems in Change-Point Analysis. Wiley, Chichester
Csörgő M, Révész P (1981) Strong Approximations in Probability and Statistics. Academic Press, New York
Doukhan P, Oppenheim G, Taqqu MS (2003) Theory and applications of long-range dependence. Birkhäuser, Boston
Gombay E, Horváth L, Hušková M (1996) Estimators and tests for change in variances. Statistics & Decisions 14, 145–159
Granger CW, Joyeux R (1980) An introduction to long-range time series models and fractional differencing. J. Time Ser. Anal. 1, 15–30
Ho HC, Hsing T (1997) Limit theorems for functionals of moving averages. Ann. Probab. 25, 1636–1669
Horváth L, Kokoszka P (1997) The effect of long-range dependence on change-point estimators. J. Statist. Planning Inference 64, 57–81
Hosking JRM (1981) Fractional differencing. Biometrika 68, 165–176
Inclán C, Tiao GC (1994) Use of cumulative sums of squares for retrospective detection of change of variance. J. Amer. Statist. Assoc. 89, 913–923
Kokoszka P, Leipus R (2003) Detection and estimation of changes in regime. In: Theory and applications of long-range dependence (Doukhan P, Oppenheim G, Taqqu MS Eds.), Birkhäuser, Boston, 325–337
Koul HL, Surgailis D (2002) Asymptotic expansion of the empirical process of long memory moving averages. In: Empirical process techniques for dependent data, edited by H. Dehling, T. Mikosch and M. Sørensen. Birkhäuser, Boston, 213–239.
Lo AW (1991) Long-term memory in stock market prices. Econometrica 59, 1279–1313
Mori T, Oodaira H (1987) The functional iterated logarithm law for stochastic processes represented by multiple Wiener integrals. Probab. Theory Related Fields 76, 299–310
Robinson PM (1994a) Time series with strong dependence. In: Advances in Econometrics Sixth World Congress (Sims CA Ed.), Cambridge Univ. Press, Vol. 1, 47–95
Robinson PM (1994b) Semiparametric analysis of long-memory time series. Ann. Statist. 22, 515–539
Samorodnitsky G, Taqqu MS (1994) Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance. Chapman and Hall, London
Surgailis D (1982) Zones of attraction of self-similar multiple integrals. Lithuanian Math. J. 22, 327–340
Taqqu MS (1975) Weak convergence to fractional Brownian motion and to the Rosenblatt process. Z. Wahrschein. verw. Gebiete 31, 287–302
Wang L (2003) Limit theorems in change-point problems with multivariate long-range dependent observations. Statistics & Decisions 21, 219–236
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This research is partly supported by NSFC Grants and SRF for ROCS, SEM.
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Wang, L., Wang, J. Change-of-variance problem for linear processes with long memory. Statistical Papers 47, 279–298 (2006). https://doi.org/10.1007/s00362-005-0288-1
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DOI: https://doi.org/10.1007/s00362-005-0288-1