Structural breaks in time series

Journal of Time Series Analysis

Volumn 34, Issue 1, 2013, Pages 1-16

  Aue, Alexander ^a   Horváth, Lajos ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF UTAH   (United States)

Author keywords

Change points; CUSUM; Long memory; Mean change; Unit root; Variance change

Indexed keywords

EID: 84871607548     PISSN: 01439782     EISSN: 14679892     Source Type: Journal    
DOI: 10.1111/j.1467-9892.2012.00819.x     Document Type: Review

References (126)

1. Adak, S. (1998) Time dependent spectral analysis of non-stationary time series. Journal of the American Statistical Association 93, 1488-1501.
2. Altissimo, F. and Corradi, V. (2003) Strong rules for detecting the number of breaks in a time series. Journal of Econometrics 117, 207-44.
3. Andreou, E. and Ghysels, E. (2002) Detecting multiple breaks in financial market volatility dynamics. Journal of Applied Econometrics 17, 579-600.
4. Andreou, E. and Ghysels, E. (2009) Structural breaks in financial time series. In: Handbook of Financial Time Series, (eds T. G. Andersen et al.). Berlin: Springer-Verlag, pp. 839-70.
5. Andrews, D. W. K. (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817-58.
6. Andrews, D. W. K. (1993) Tests for parameter instability and structural change with unknown change point. Econometrica 61, 821-56.
7. Aue, A., Berkes, I. and Horváth, L. (2006a) Strong approximation for the sums of squares of augmented GARCH sequences. Bernoulli 12, 583-608.
8. Aue, A., Gabrys, R., Horváth, L. and Kokoszka, P. (2009a) Estimation of a change-point in the mean function of functional data. Journal of Multivariate Analysis 100, 2254-69.
9. Aue, A., Hörmann, S., Horváth, L., Hušková, M. and Steinebach, J. Sequential testing for the stability of high frequency portfolio betas. Econometric Theory 28, 804-37.
10. Aue, A., Hörmann, S., Horváth, L. and Reimherr, M. (2009b) Break detection in the covariance structure of multivariate nonlinear time series models. The Annals of Statistics 37, 4046-87.
11. Aue, A. and Horváth, L. (2004) Delay time in sequential detection of change. Statistics & Probability Letters 67, 221-31.
12. Aue, A., Horváth, L., and Hušková, M. (2009c) Extreme value theory for stochastic integrals of Legendre polynomials. Journal of Multivariate Analysis 100, 1029-43.
13. Aue, A., Horváth, L. and Hušková, M. (2012) Segmenting mean-nonstationary time series via trending regressions. Journal of Econometrics 168, 367-81.
14. Aue, A., Horváth, L., Hušková, M. and Kokoszka, P. (2006b) Change-point monitoring in linear models. Econometrics Journal 9, 373-403.
15. Aue, A., Horváth, L., Hušková, M. and Kokoszka, P. (2008a) Testing for changes in polynomial regression. Bernoulli 14, 637-60.
16. Aue, A., Horváth, L., Hušková, M. and Ling, S. (2009d) On distinguishing between random walk and change in the mean alternatives. Econometric Theory 25, 411-41.
17. Aue, A., Horváth, L., Kokoszka, P. and Steinebach, J. (2008b) Monitoring shifts in mean: asymptotic normality of stopping times. Test 17, 515-30.
18. Aue, A., Horváth, L. and Reimherr, M. (2009e) Delay times of sequential procedures for multiple time series regression models. Journal of Econometrics 149, 174-90.
19. Aue, A., and Lee, T. C. M. (2011) On image segmentation using information theoretic criteria. The Annals of Statistics 39, 2912-35.
20. Baek, C. and Pipiras, V. (2012) Statistical tests for a single change in mean against long-range dependence. Journal of Time Series Analysis 33, 131-51.
21. Bai, J. (1993) On the partial sums of residuals in autoregressive and moving average models. Journal of Time Series Analysis 14, 247-60.
22. Bai, J. (1997) Estimating multiple breaks one at a time. Econometric Theory 13, 315-52.
23. Bai, J. (1999) Likelihood ratio tests for multiple structural changes. Journal of Econometrics 91, 299-323.
24. Bai, J., and Perron, P. (1998) Estimating and testing linear models with multiple structural changes. Econometrica 66, 47-78.
25. Banerjee, A., and Urga, G. (2005) Modelling structural breaks, long memory and stock market volatility: an overview. Journal of Econometrics 129, 1-34.
26. Barry, D. and Hartigan, J. A. (1993) A Bayesian analysis for change point problems. Journal of the American Statistical Association 88, 309-19.
27. Berkes, I., Gabrys, R., Horváth, L. and Kokoszka, P. (2009a) Detecting changes in the mean of functional observations. Journal of the Royal Statistical Society, Series B 71, 927-46.
28. Berkes, I., Gombay, E. and Horváth, L. (2009b) Testing for changes in the covariance structure of linear processes. Journal of Statistical Planning and Inference 139, 2044-63.
29. Berkes, I., Gombay, E., Horváth, L. and Kokoszka, P. (2004) Sequential change-point detection in GARCH(p, q) models. Econometric Theory 20, 1140-67.
30. Berkes, I., Hörmann, S. and Horváth, L. (2008) The functional central limit theorem for a family of GARCH observations with applications. Statistics & Probability Letters 78, 2725-30.
31. Berkes, I., Horváth, L., Kokoszka, P. and Shao, Q.-M. (2006) On discriminating between long-range dependence and changes in the mean. The Annals of Statistics 34, 1140-65.
32. Bernard, J.-T., Idoudi, N., Khalaf, L. and Yélou, C. (2007) Finite sample multivariate structural change tests with application to energy demand models. Journal of Econometrics 141, 1229-44.
33. Bhattacharya, R. N., Gupta, V. K. and Waymire, E. (1983) The Hurst effect under trends. Journal of Applied Probability 20, 649-67.
34. Billingsley, P. (1968) Convergence of Probability Measures. New York: Wiley.
35. Bollerslev, T. (1986) Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31, 307-27.
36. Bradley, R. C. (2007) Introduction to Strong Mixing Conditions Vol.1-3.. Heber City, UT: Kendrick Press.
37. Brodsky, B. E. and Darkhovsky, B. S. (1993) Nonparametric Methods in Change-Point Problems. Dordrecht: Kluwer.
38. Carlstein, E., Müller, H.-G. and Siegmund, D. (1994) Change-Point Problems. IMS Lecture Notes-Monograph Series, Vol. 23. Hayward, CA.
39. Cavaliere, G. and Taylor, R. A. M. (2008) Testing for a change in persistence in the presence of non-stationary volatility. Journal of Econometrics 147, 84-98.
40. Chib, S. (1998) Estimation and comparison of multiple change-point models. Journal of Econometrics 86, 221-41.
41. Chu, C.-S.J., Hornik, K. and Kuan, C.-M. (1995) MOSUM tests for parameter constancy. Biometrika 82, 603-17.
42. Chu, C.-S.J., Hornik, K. and Kuan, C.-M. (1995) The moving-estimates test for parameter stability. Econometric Theory 11, 699-720.
43. Chu, C.-S.J., Stinchcombe, M. and White, H. (1996) Monitoring structural change. Econometrica 64, 1045-65.
44. Cso{double acute}rgo{double acute}, M. and Horváth, L. (1997) Limit Theorems in Change-Point Analysis. Chichester: Wiley.
45. Darling, D. A. and Erdo{double acute}s, P. (1956) A limit theorem for the maximum of normalized sums of independent random variables. Duke Mathematics Journal 23, 143-55.
46. Davis, R. A., Huang, D. and Yao, Y.-C. (1995) Testing for a change in the parameter values and order of an autoregressive model. The Annals of Statistics 23, 282-304.
47. Davis, R. A., Lee, T. C. M. and Rodriguez-Yam, G. (2006) Structural break estimation for nonstationary time series models. Journal of the American Statistical Association 101, 223-39.
48. Dedecker, J., Doukhan, P., Lang, G., León, R. J. R., Louhichi, S. and Prieur, C.. (2007) Weak Dependence with Applications and Examples. Lecture Notes in Statistics 190. New York: Springer.
49. Döring, M. (2011) Convergence in distribution of multiple change point estimators. Journal of Statistical Planning and Inference 141, 2238-48.
50. Einmahl, U. (1989) The Darling-Erdo{double acute}s theorem for sums of i.i.d. random variables. Probability Theory and Related Fields 82, 241-57.
51. Engle, R. F. (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50, 987-1007.
52. Francq, C. and Zakoïan, J.-M. (2010) GARCH Models. Chichester: Wiley.
53. Ghysels, E., Guay, A., and Hall, A. (1997) Predictive tests for structural change with unknown breakpoint. Journal of Econometrics 82, 209-33.
54. Giraitis, L., Kokoszka, P. and Leipus, R. (2001) Testing for long memory in the presence of a general trend. Journal of Applied Probability 38, 1033-54.
55. Giraitis, L., Kokoszka, P., Leipus, R. and Teyssiére, G. (2003) Rescaled variance and related tests for long memory in volatility and levels. Journal of Econometrics 112, 265-94.
56. Gombay, E. and Horváth, L. (1990) Asymptotic distributions of maximum likelihood tests for change in the mean. Biometrika 77, 411-14.
57. Gombay, E. and Horváth, L. (1994) An application of the maximum likelihood test to the change-point problem. Stochastic Processes and Their Applications 50, 161-71.
58. Gombay, E. and Horváth, L. (1996) On the rate of approximations for maximum likelihood tests in change-point models. Journal of Multivariate Analysis 56, 120-52.
59. Gombay, E. and Serban, D. (2009) Monitoring parameter change in AR(p) time series models. Journal of Multivariate Analysis 100, 715-25.
60. Gombay, E., Horváth, L. and Hušková, M. (1996) Estimators and tests for change in variances. Statistics & Decisions 14, 145-59.
61. Granger, C. W. J. and Joyeux, R. (1980) An introduction to long-memory time series models and fractional differencing. Journal of Time Series Analysis 1, 15-29.
62. Gut, A. and Steinebach, J. (2002) Truncated sequential change-point detection based on renewal counting processes. Scandinavian Journal of Statistics 29, 693-719.
63. Gut, A. and Steinebach, J. (2009) Truncated sequential change-point detection based on renewal counting processes II. Journal of Statistical Planning and Inference 139, 1921-36.
64. Hall, P. G. (1979) On the rate of convergence of normal extremes. Journal of Applied Probability 16, 433-39.
65. Hansen, B. E. (2000) Testing for structural change in conditional models. Journal of Econometrics 97, 93-115.
66. Harvey, D. I., Leybourne, S. J. and Taylor, R. A. M. (2009) Simple, robust, and powerful tests of the breaking trend hypothesis. Econometric Theory 25, 995-1029.
67. Harvey, D. I., Leybourne, S. J. and Taylor, R. A. M. (2010) Robust methods for detecting multiple level breaks in autocorrelated time series. Journal of Econometrics 157, 342-58.
68. Hidalgo, J. and Robinson, P. M. (1996) Testing for structural change in a long-memory environment. Journal of Econometrics 70, 159-74.
69. Hörmann, S. and Kokoszka, P. (2010) Weakly dependent functional data. The Annals of Statistics 38, 1845-84.
70. Horváth, L. (1993) The maximum likelihood method for testing changes in the parameters of normal observations. The Annals of Statistics 2, 671-80.
71. Horváth, L., Hušková, M. and Kokoszka, P. (2010) Testing the stability of the functional autoregressive process. Journal of Multivariate Analysis 101, 352-67.
72. Horváth, L., Hušková, M., Kokoszka, P. and Steinebach, J. (2004) Monitoring changes in linear models. Journal of Statistical Planning and Inference 126, 225-51.
73. Horváth, L. and Kokoszka, P. (2012) Inference for Functional Data with Applications. New York: Springer.
74. Horváth, L., Kokoszka, P. and Steinebach, J. (1999) Testing for changes in multivariate dependent observations with an application to temperature changes. Journal of Multivariate Analysis 68, 96-119.
75. Hosking, J. R. M. (1981) Fractional differencing. Biometrika 68, 165-76.
76. Hušková, M. (2004) Permutation principle and bootstrap in change point analysis. In Asymptotic Methods in Stochastics. (eds L. Horváth, and B. Szyszkowicz, ). Providence, RI: Fields Institute Communications 44, American Mathematical Society, pp. 273-91.
77. Hušková, M., and Kirch, C. (2012) Bootstrapping sequential cange-point tests for linear regression. Metrika 75, 673-708.
78. Hušková M. and Picek J. (2005) Bootstrap in detection of changes in linear regression. Sankhy: The Indian Journal of Statistics 67, 1-27.
79. Hušková, M., Prášková, Z. and Steinebach, J. (2007) On the detection of changes in autoregressive time series I. Asymptotics. Journal of Statistical Planning and Inference 137, 1243-59.
80. Inclán, C. and Tiao, G. C. (1994) Use of cumulative sums of squares for retrospective detection of change of variance. Journal of the American Statistical Association 89, 913-23.
81. Juhl, T. and Xiao, Z. (2009). Testing for changing mean monotonic power. Journal of Econometrics 48, 14-24.
82. Kim, T.-H., Leybourne, S. and Newbold, P. (2002) Unit root tests with a break in innovation variance. Journal of Econometrics 109, 365-87.
83. King, A. and Romlogan-Dobson, C. (2011) Nonlinear time-series convergence: The role of structural breaks. Economics Letters 110, 238-40.
84. Kirch, C. (2008) Bootstrapping sequential change-point tests. Sequential Analysis 27, 330-49.
85. Kokoszka, P. and Leipus, R. (2000) Change-point estimation in ARCH models. Bernoulli 6, 513-39.
86. Kuan, C.-M. and Hornik, K. (2005) The generalized fluctuation test: A unifying view. Econometric Reviews 82, 603-17.
87. Kühn, C. (2001) An estimator of the number of change-points based on a weak invariance principle. Statistics & Probability Letters 51, 189-96.
88. Kulperger, R. J. (1985) On the residuals of autoregressive processes and polynomial regression. Stochastic Processes and their Applications 21, 107-18.
89. Kurozumi, E. and Tuvaandorj, P. (2011) Model selection criteria in multivariate models with multiple structural changes. Journal of Econometrics 164, 218-38.
90. Kwiatkowski, D., Phillips, P. C. B., Schmidt, P. and Shin, Y. (1992) Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root?. Journal of Econometrics 54, 159-78.
91. Lavielle, M. and Ludena, C. (2000) The multiple change-points problem for the spectral distribution. Bernoulli 6, 845-69.
92. Lazarová, S. (2005) Testing for structural change in regression with long memory errors. Journal of Econometrics 129, 329-72.
93. Lee, S. and Park, S. (2001) The cusum of squares test for scale changes in infinite order moving average processes. Scandinavian Journal of Statistics 28, 625-44.
94. Leisch, F., Hornik, K. and Kuan, C. M. (2000) Monitoring structural changes with the generalized fluctuation test. Econometric Theory 16, 835-54.
95. Liu, W. and Wu, W. B. (2010) Asymptotics of spectral density estimates. Econometric Theory 26, 1218-45.
96. Lo, A. (1991) Long-term memory in stock market prices. Econometrica 59, 1279-1313.
97. Lu, Q., Lund, R. and Lee, T. C. M. (2010) An MDL approach to the climate segmentation problem. The Annals of Applied Statistics 4, 299-319.
98. Ohanessian, A., Russell, J. R. and Tsay, R. S. (2008) True or spurious long memory? A new test. Journal of Business & Economic Statistics 26, 161-75.
99. Ombao, H. C., Raz, J. A., von Sachs, R. and Malow, B. A. (2001) Automatic statistical analysis of bivariate nonstationary time series. Journal of the American Statistical Association 96, 543-60.
100. Page, E. S. (1954) Continuous inspection schemes. Biometrika 41, 100-5.
101. Page, E. S. (1955) A test for a change in a parameter occurring at an unknown point. Biometrika 42, 523-27.
102. Pawlak, M., Rafajlowicz, E. and Steland, A.(2010). Nonparametric sequential change-point detection by a vertically trimmed box method. IEEE Transactions on Information Theory 56, 3621-3634
103. Perron, P. (2006) Dealing with structural breaks. In Palgrave Handbook of Econometrics, Vol. 1, (eds K. Patterson, and T. C. Mills, ). xxxx: Palgrave Macmillan, pp. 278-352.
104. Picard, D. (1985) Testing and estimating change-points in time series. Advances in Applied Probability 17, 841-67.
105. Qu, Z. (2011) A test against spurious long memory. Journal of Business & Economic Statistics 29, 423-38.
106. Qu, Z. and Perron, P. (2007) Estimating and testing structural changes in multivariate regressions. Econometrica 75, 459-502.
107. Ramsay, J. O., and Silverman, B. W. (2005) Functional Data Analysis, 2nd ed. New York: Springer.
108. Reeves, J., Chen, J., Wang, X. L., Lund, R. B. and Lu, Q. (2007) A review and comparison of changepoint detection techniques for climate data. Journal of Applied Meteorology and Climatology 46, 900-15.
109. Robbins, M., Gallagher, C., Lund, R. and Aue, A. (2011) Mean shift testing in correlated data. Journal of Time Series Analysis 32, 498-511.
110. Robbins, M. W., Lund, R. B., Gallagher, C. M. and Lu, Q. (2011) Changepoints in the North Atlantic tropical cyclone record. Journal of the American Statistical Association 106, 89-99.
111. Schwarz, G. (1978) Estimating the dimension of a model. The Annals of Statistics 6, 461-64.
112. Serbinovska, M. (1996) Consistency of an estimator of the number of changes in binomial observations. Statistics & Probability Letters 29, 337-44.
113. Shao, X. (2011) A simple test of changes in the mean in the possible presence of long-range dependence. Journal of Time Series Analysis 32, 598-606.
114. Shao, X. and Zhang, X. (2010) Testing for change points in time series. Journal of the American Statistical Association 105, 1228-40.
115. Shorack, G. R. and Wellner, J. A. (1986) Empirical Processes with Applications to Statistics. New York: Wiley.
116. Steland, A. (2007) Monitoring procedures to detect unit roots and stationarity. Econometric Theory 23, 1108-35.
117. Stoumbos, Z. G., Reynolds Jr. M. R., Ryan, T. T. P., Woodall, W. H. (2000) The state of statistical process control as we proceed into the 21st century. Journal of the American Statistical Association 95, 992-8.
118. Tang, S. M. and MacNeill, I. B. (1993) The effect of serial correlation on tests for parameter change at unknown time. The Annals of Statistics 21, 552-75.
119. Vostrikova, L. Ju. (1981) Detection of ''disorder'' in a Wiener process. Theory of Probability and its Applications 26, 356-62.
120. Wied, D., Krämer, W. and Dehling, H. (2012)Testing for a change in correlation at an unknown point in time using an extended functional delta method. Econometric Theory 28, 570-89.
121. Wu, W. B. (2007) Strong invariance principles for dependent random variables. The Annals of Probability 35, 2294-320.
122. Yamaguchi, K. (2011) Estimating a change point in the long memory parameter. Journal of Time Series Analysis 32, 304-14.
123. Yao, Y.-C. (1988) Estimating the number of change-points via Schwarz' criterion. Statistics & Probability Letters 6, 181-9.
124. Yoon, G. (2005) Long-memory property of nonlinear transformations of break processes. Economics Letters 87, 373-7.
125. Yu, H. (2007) High moment partial sum processes of residuals in ARMA models and their applications. Journal of Time Series Analysis 28, 72-91.
126. Zeileis, A., Leisch, F., Kleiber, C. and Hornik, K. (2005) Monitoring structural change in dynamic econometric models. Journal of Applied Econometrics 20, 99-121.