×

zbMATH — the first resource for mathematics

Comments on: “Extensions of some classical methods in change point analysis”. (English) Zbl 1305.62312
Summary: First of all, we would like to congratulate and to thank L. Horváth and G. Rice [Test 23, No. 2, 219–255 (2014; Zbl 1305.62310)] for providing an excellent overview of a recent development in the area of change point. This area is developing quite fast with many new procedures, many new theoretical results and many applications. We appreciate that the paper brings extension of existing empirical processes techniques to time series and numerical examples giving the performance for finite sample setups as well as demonstrations of the discussed methods on real data. In the following, we would like to make several remarks on the topics that were discussed in the paper only very briefly.

MSC:
62M07 Non-Markovian processes: hypothesis testing
60F17 Functional limit theorems; invariance principles
62L20 Stochastic approximation
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P20 Applications of statistics to economics
62F05 Asymptotic properties of parametric tests
62P12 Applications of statistics to environmental and related topics
Software:
wbs; basta
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Antoch J, Hušková M (2001a) M-estimators of structural changes in regression models. Tatra Mt Math 22:197–208 · Zbl 0991.62045
[2] Antoch J, Hušková M (2001b) Permutation tests for change point analysis. Stat Probab Lett 53:37–46 · Zbl 0980.62033
[3] Antoch J, Hušková M, Gregoire G (2007) Tests for continuity of regression function. J Stat Plan Inference 137:753–777 · Zbl 1104.62037
[4] Antoch J, Jarušková D (2013) Testing for multiple change points. Comput Stat 28:2161–2183 · Zbl 1306.65022
[5] Aue A, Cheung R, Lee TCM, Zhong M (2014) Segmented model selection in quantile regression using the minimum description length principle (preprint) · Zbl 1368.62092
[6] Bai J, Perron P (1998) Estimating and testing linear models with multiple structural changes. Econometrica 66:47–78 · Zbl 1056.62523
[7] Bai J, Perron P (2003a) Computation and analysis of multiple structural change models. J Appl Econom 18:1–22
[8] Bai J, Perron P (2003b) Critical values for multiple structural change tests. Econom J 6:72–78 · Zbl 1032.62064
[9] Cho H, Fryzlewicz P (2012) Multiple change-point detection for high-dimensional time series via sparsified binary segmentation (preprint)
[10] Chochola O, Hušková M, Prášková Z, Steinebach J (2013) Robust monitoring of CAPM portfolio betas. J Multivar Anal 115:374–395 · Zbl 1271.62057
[11] Ciuperca G (2009) The M-estimation in multiple-phase random nonlinear model. Stat Probab Lett 75:573–580 · Zbl 1156.62314
[12] Ciuperca G (2011a) A general criterion to determine the number of change-points. Stat Probab Lett 81:1267–1275 · Zbl 1219.62110
[13] Ciuperca G (2011b) Estimating nonlinear regression with and without change points by the LAD. Ann Inst Stat Math 63:717–743 · Zbl 1230.62089
[14] Ciuperca G (2011c) Penalized least absolute deviations estimation for nonlinear model with change-points. Stat Pap 52:371–390 · Zbl 1247.62076
[15] Cuiperca G (2013) Two tests for sequential detection of a change-point in a nonlinear model. J Stat Plan Inference 143:1719–1743 · Zbl 1432.62272
[16] Ciuperca G (2014) Model selection by LASSO methods in a change-point model. Stat Pap. doi: 10.1007/s00362-012-0482-x · Zbl 1297.62162
[17] Dehling H, Fried R (2012) Asymptotic distribution of two-sample empirical U-quantiles with applications to tests for structural change. J Multivar Anal 105:124–140 · Zbl 1250.62021
[18] Dehling H, Rooch A, Taqqu MS (2013) Non-parametric change-point tests for long-range dependent data. Scand J Stat 40:153–173 · Zbl 1259.62028
[19] Fiteni I (2002) Robust estimation of structural break points. Econom Theory 18:349–386 · Zbl 1109.62306
[20] Frick K, Munk A, Sieling H (2014) Multiscale change point inference. J R Stat Soc Ser B (to appear)
[21] Fryzlewicz P (2012) Wild binary segmentation for multiple change-point detection. London School of Economics and Political Science, London (Technical Report) · Zbl 1302.62075
[22] Fryzlewicz P, Subba Rao S (2014) Multiple-change-point detection for auto-regressive conditional heteroscedastic processes. J R Stat Soc Ser B (to appear)
[23] Gombay E, Hušková M (1998) Rank based estimators of the change point. J Stat Plan Inference 67:137–154 · Zbl 0932.62038
[24] Harchaoui Z, Levy-Leduc C (2010) Multiple change-point estimation with a total variation penalty. J Am Stat Assoc 105:1480–1493 · Zbl 1388.62211
[25] Hlávka Z, Hušková M, Kirch C, Meintanis S (2012) Monitoring changes in the error distribution of autoregressive models based on Fourier methods. TEST 21:605–634 · Zbl 1284.62557
[26] Hlávka Z, Hušková M, Kirch C, Meintanis S (2014) Bootstrap procedures for sequential change point analysis in autoregressive models. Commun Stat Simul Comput (accepted)
[27] Hušková M (1997) Limit theorems for rank statistics. Stat Probab Lett 32:45–55 · Zbl 0933.62039
[28] Hušková M (2004) Permutation principle and bootstrap in change point analysis. In: Asymptotic methods stochastics, Fields Institute Communications, vol 44, pp 273–291 · Zbl 1067.62044
[29] Hušková M (2013) Robust change point analysis. In: Becker C, Fried R, Kuhnt S (eds) Robustness and complex data structures: Festschrift in honour of Ursula Gather. Springer, Berlin, pp 171–190
[30] Hušková M, Kirch C (2008) Bootstrapping confidence intervals for the change point of time series. J Time Ser Anal 29:947–972 · Zbl 1194.62063
[31] Hušková M, Kirch C (2010) A note on studentized confidence intervals for the change-point. Comput Stat 25:269–289 · Zbl 1223.62147
[32] Hušková M, Kirch C (2012) Bootstrapping sequential change-point tests for linear regression. Metrika 75:673–708 · Zbl 1362.62161
[33] Hušková M, Kirch C, Prášková Z, Steinebach J (2008) On detection of changes in autoregressive time series II: resampling procedures. J Stat Plan Inference 138:1697–1721 · Zbl 1131.62079
[34] Hušková M, Marušiaková M (2012) M-procedures for detection of changes for dependent observations. Commun Stat Simul Comput 41:1032–1050 · Zbl 1347.62071
[35] Hušková M, Meintanis S (2006) Change point analysis based on empirical characteristic functions. Metrika 63:145–168 · Zbl 1141.62317
[36] Hušková M, Picek J (2005) Bootstrap in detection of changes in linear regression. Sankhya 67:200–226
[37] Kim HJ, Yu B, Feuer EJ (2009) Selecting the number of change-points in segmented line regression. Statistica Sinica 19:597–609 · Zbl 1168.62037
[38] Kirch C (2007) Block permutation principles for the change analysis of dependent data. J Stat Plan Inference 137:2453–2474 · Zbl 1274.62320
[39] Kirch C (2008) Bootstrapping sequential change-point tests. Seq Anal 27:330–349 · Zbl 1145.62060
[40] Kirch C, Steinebach J (2006) Permutation principles for the change analysis of stochastic processes under strong invariance. J Comput Appl Math 186:64–88 · Zbl 1074.62030
[41] Kirch C, Muhsal B (2011) Change-point methods for multiple structural breaks and hidden Markov models (preprint)
[42] Lavielle M, Teyssiere G (2006) Detection of multiple change-points in multivariate time series. Lith Math J 46:287–306 · Zbl 1138.62051
[43] Lavielle M, Teyssiere G (2007) Adaptive detection of multiple change-points in asset price volatility. In: Teyssiere G, Kirman AP (eds) Long memory in economics. Springer, Heidelberg, pp 129–156 · Zbl 1181.91348
[44] Lee C-B (1995) Estimating the number of change points in a sequence of independent normal random variables. Stat Probab Lett 25:241–248 · Zbl 0839.62015
[45] Lu Q, Lund R, Lee TCM (2010) An MDL approach to the climate segmentation problem. Ann Appl Stat 4:299–319 · Zbl 1189.62180
[46] Neumeyer N, Van Keilegom I (2009) Changepoint tests for the error distribution in nonparametric regression. Scand J Stat 36:518–541 · Zbl 1195.62054
[47] Pan J, Chen J (2006) Application of modified information criterion to multiple change point problems. J Multivar Anal 97:2221–2241 · Zbl 1101.62050
[48] Prášková Z, Chochola O (2014) M-procedures for detection of a change under weak dependence. J Stat Plan Inference (to appear). http://dx.doi.org/10.1016/j.jspi.2014.01.006 · Zbl 1285.62022
[49] Preuß P, Puchstein R, Dette H (2013) Detection of multiple structural breaks in multivariate time series. arXiv:1309.1309
[50] Sen PK (1978) Invariance principles for rank statistics revisited. Sankhya Ser A 40:215–236 · Zbl 0439.62006
[51] Vostrikova L (1981) Detecting ’disorder’ in multidimensional random processes. Sov Math Dokl 24:55–59 · Zbl 0487.62072
[52] Yao Y-C (1988) Estimating the number of change-points via Schwarz criterion. Stat Probab Lett 6:181–189 · Zbl 0642.62016
[53] Yao Y-C (1990) On asymptotic behavior of a class of nonparametric tests. Stat Probab Lett 9:173–177 · Zbl 0686.62030
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.