Korkas, Karolos K. Ensemble binary segmentation for irregularly spaced data with change-points. (English) Zbl 1485.62121 J. Korean Stat. Soc. 51, No. 1, 65-86 (2022). Summary: We propose a new technique for consistent estimation of the number and locations of the change-points in the structure of an irregularly spaced time series. The core of the segmentation procedure is the ensemble binary segmentation method (EBS), a technique in which a large number of multiple change-point detection tasks using the binary segmentation method are applied on sub-samples of the data of differing lengths, and then the results are combined to create an overall answer. We do not restrict the total number of change-points a time series can have, therefore, our proposed method works well when the spacings between change-points are short. Our main change-point detection statistic is the time-varying autoregressive conditional duration model on which we apply a transformation process in order to decorrelate it. To examine the performance of EBS we provide a simulation study for various types of scenarios. A proof of consistency is also provided. Our methodology is implemented in the R package eNchange, available to download from CRAN. MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) Keywords:multiple change-point detection; conditional duration models; binary segmentation; ensemble methods; non-stationarity Software:CRAN; R; wbs; eNchange; basta; wbsts PDFBibTeX XMLCite \textit{K. K. Korkas}, J. Korean Stat. Soc. 51, No. 1, 65--86 (2022; Zbl 1485.62121) Full Text: DOI arXiv References: [1] Anastasiou, A., & Fryzlewicz, P. (2019). Detecting multiple generalized change-points by isolating single ones. arXiv:1901.10852 (arXiv preprint). · Zbl 07472633 [2] Baranowski, R.; Chen, Y.; Fryzlewicz, P., Narrowest-over-threshold detection of multiple change-points and change-point-like features, Journal of the Royal Statistical Society Series B, 20, 649-672 (2019) · Zbl 1420.62157 [3] Cho, H.; Fryzlewicz, P., Multiscale and multilevel technique for consistent segmentation of nonstationary time series, Statistica Sinica, 22, 207-229 (2012) · Zbl 1417.62240 [4] Cho, H., & Korkas, K. (2018). High-dimensional garch process segmentation with an application to value-at-risk. arXiv:1706.01155 (arXiv preprint). [5] Davidson, J., Stochastic limit theory: An introduction for econometricians (1994), OUP · Zbl 0904.60002 [6] Davis, R.; Huang, D.; Yao, Y., Testing for a change in the parameter values and order of an autoregressive model, Annals of Statistics, 23, 282-304 (1995) · Zbl 0822.62072 [7] Douc, R.; Moulines, E.; Stoffer, D., Nonlinear time series: Theory, methods and applications with R examples (2014), Chapman and Hall · Zbl 1306.62026 [8] Engle, RF; Russell, JR, Autoregressive conditional duration: A new model for irregularly spaced transaction data, Econometrica, 20, 1127-1162 (1998) · Zbl 1055.62571 [9] Francq, C.; Roussignol, M.; Zakoian, J-M, Conditional heteroskedasticity driven by hidden Markov chains, Journal of Time Series Analysis, 22, 2, 197-220 (2001) · Zbl 0972.62077 [10] Fryzlewicz, P., Wild binary segmentation for multiple change-point detection, The Annals of Statistics, 42, 6, 2243-2281 (2014) · Zbl 1302.62075 [11] Fryzlewicz, P., Detecting possibly frequent change-points: Wild binary segmentation 2 and steepest-drop model selection, Journal of the Korean Statistical Society, 20, 1-44 (2020) [12] Fryzlewicz, P.; Subba Rao, S., Mixing properties of arch and time-varying arch processes, Bernoulli, 17, 1, 320-346 (2011) · Zbl 1284.62550 [13] Fryzlewicz, P.; Subba Rao, S., Multiple-change-point detection for auto-regressive conditional heteroscedastic processes, Journal of the Royal Statistical Society Series B, 20, 903-924 (2014) · Zbl 1411.62248 [14] Harchaoui, Z.; Lévy-Leduc, C., Multiple change-point estimation with a total variation penalty, Journal of the American Statistical Association, 105, 492, 1480-1493 (2010) · Zbl 1388.62211 [15] Hawkes, AG, Point spectra of some mutually exciting point processes, Journal of the Royal Statistical Society Series B (Methodological), 33, 3, 438-443 (1971) · Zbl 0238.60094 [16] Inclan, C.; Tiao, GC, Use of cumulative sums of squares for retrospective detection of changes of variance, Journal of the American Statistical Association, 89, 913-923 (1994) · Zbl 0825.62678 [17] Killick, R.; Fearnhead, P.; Eckley, IA, Optimal detection of changepoints with a linear computational cost, Journal of the American Statistical Association, 107, 500, 1590-1598 (2012) · Zbl 1258.62091 [18] Kokoszka, P., & Teyssière, G. (2002). Change-point detection in garch models: Asymptotic and bootstrap tests. Technical report, Universite Catholique de Louvain. [19] Korkas, K. K. (2020). eNchange: Ensemble methods for multiple change-point detection. R Foundation for Statistical Computing. [20] Korkas, KK; Fryzlewicz, P., Multiple change-point detection for non-stationary time series using wild binary segmentation, Statistica Sinica, 27, 1, 287-311 (2017) · Zbl 1356.62143 [21] Kovács, S., Li, H., Bühlmann, P., & Munk, A. (2020). Seeded binary segmentation: A general methodology for fast and optimal change point detection. arXiv:2002.06633 (arXiv preprint). [22] Meinshausen, N.; Bühlmann, P., Stability selection, Journal of the Royal Statistical Society Series B (Statistical Methodology), 72, 4, 417-473 (2010) · Zbl 1411.62142 [23] Mercurio, D.; Spokoiny, V., Statistical inference for time-inhomogeneous volatility models, Annals of Statistics, 32, 577-602 (2004) · Zbl 1091.62103 [24] Mikosch, T.; Stărică, C., Nonstationarities in financial time series, the long-range dependence, and the igarch effects, The Review of Economics and Statistics, 86, 1, 378-390 (2004) [25] Olshen, AB; Venkatraman, E.; Lucito, R.; Wigler, M., Circular binary segmentation for the analysis of array-based dna copy number data, Biostatistics, 5, 4, 557-572 (2004) · Zbl 1155.62478 [26] Roueff, F.; Von Sachs, R.; Sansonnet, L., Locally stationary hawkes processes, Stochastic Processes and their Applications, 126, 6, 1710-1743 (2016) · Zbl 1336.60094 [27] Wang, T.; Samworth, RJ, High dimensional change point estimation via sparse projection, Journal of the Royal Statistical Society Series B (Statistical Methodology), 80, 1, 57-83 (2018) · Zbl 1439.62199 [28] Xin, L.; Zhu, M., Stochastic stepwise ensembles for variable selection, Journal of Computational and Graphical Statistics, 21, 2, 275-294 (2012) [29] Yao, Y., Estimating the number of change-points via Schwarz’ criterion, Statistics and Probability Letters, 6, 181-189 (1988) · Zbl 0642.62016 [30] Zhu, M., Use of majority votes in statistical learning, Wiley Interdisciplinary Reviews Computational Statistics, 7, 6, 357-371 (2015) 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.