# zbMATH — the first resource for mathematics

High-dimensional changepoint detection via a geometrically inspired mapping. (English) Zbl 1448.62132
Summary: High-dimensional changepoint analysis is a growing area of research and has applications in a wide range of fields. The aim is to accurately and efficiently detect changepoints in time series data when both the number of time points and dimensions grow large. Existing methods typically aggregate or project the data to a smaller number of dimensions, usually one. We present a high-dimensional changepoint detection method that takes inspiration from geometry to map a high-dimensional time series to two dimensions. We show theoretically and through simulation that if the input series is Gaussian, then the mappings preserve the Gaussianity of the data. Applying univariate changepoint detection methods to both mapped series allows the detection of changepoints that correspond to changes in the mean and variance of the original time series. We demonstrate that this approach outperforms the current state-of-the-art multivariate changepoint methods in terms of accuracy of detected changepoints and computational efficiency. We conclude with applications from genetics and finance.

##### MSC:
 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62G10 Nonparametric hypothesis testing 62P05 Applications of statistics to actuarial sciences and financial mathematics 62P10 Applications of statistics to biology and medical sciences; meta analysis
##### Software:
changepoint; changepoint.np; CRAN; ecp; InspectChangepoint; R; SP500R; wbs
Full Text:
##### References:
 [1] Bleakley, K., Vert, J.P.: The group fused Lasso for multiple change-point detection. (2011) arXiv e-prints arXiv:1106.4199 [2] Brodsky, E.; Darkhovsky, B., Nonparametric Methods in Change Point Problems. Mathematics and Its Applications (2013), Berlin: Springer, Berlin [3] Eckley, IA; Fearnhead, P.; Killick, R.; Barber, D.; Cemgil, AT; Chiappa, S., Analysis of changepoint models, Bayesian Time Series Models chap 10, 205-224 (2011), Cambridge: Cambridge University Press, Cambridge [4] Enikeeva, F.; Harchaoui, Z., High-dimensional change-point detection under sparse alternatives, Ann. Stat., 4, 2051-2079 (2019) · Zbl 1427.62036 [5] Fearnhead, P.; Maidstone, R.; Letchford, A., Detecting changes in slope with an $$l_0$$ penalty, J. Comput. Gr. Stat., 28, 2, 1-11 (2018) [6] Fisch, A.T.M., Eckley, I.A., Fearnhead, P.: A linear time method for the detection of point and collective anomalies. arXiv e-prints arXiv:1806.01947 (2018) [7] Foret, P.: SP500R: Easy loading of SP500 stocks data. Github R package version 0.1.0 (2019) [8] Fryzlewicz, P., Wild binary segmentation for multiple change-point detection, Ann. Stat., 42, 6, 2243-2281 (2014) · Zbl 1302.62075 [9] Haynes, K., Killick, R.: changepoint.np: Methods for nonparametric changepoint detection. CRAN R package version 1.0.1 (2016) [10] Haynes, K.; Eckley, IA; Fearnhead, P., Computationally efficient changepoint detection for a range of penalties, J. Comput. Gr. Stat., 26, 1, 134-143 (2017) [11] Haynes, K.; Fearnhead, P.; Eckley, I., A computationally efficient nonparametric approach for changepoint detection, Stat. Comput., 27, 5, 1293-1305 (2017) · Zbl 06737712 [12] Horváth, L.; Hušková, M., Change-point detection in panel data, J. Time Ser. Anal., 33, 4, 631-648 (2012) · Zbl 1282.62181 [13] James, NA; Matteson, DS, ecp: An R package for nonparametric multiple change point analysis of multivariate data, J. Stat. Softw., 62, 7, 1-25 (2014) [14] Jirak, M., Uniform change point tests in high dimension, Ann. Stat., 43, 6, 2451-2483 (2015) · Zbl 1327.62467 [15] Killick, R.; Eckley, IA, changepoint: An R package for changepoint analysis, J. Stat. Softw., 58, 3, 1-19 (2014) [16] Killick, R.; Fearnhead, P.; Eckley, IA, Optimal detection of changepoints with a linear computational cost, J. Am. Stat. Assoc., 107, 500, 1590-1598 (2012) · Zbl 1258.62091 [17] Killick, R., Haynes, K., Eckley, I.A.: changepoint: An R package for changepoint analysis. CRAN R package version 2.2.2 (2016) [18] Maboudou-Tchao, EM; Hawkins, DM, Detection of multiple change-points in multivariate data, J. Appl. Stat., 40, 9, 1979-1995 (2013) [19] Mahalanobis, PC, On the Generalized Distance in Statistics (1936), India: National Institute of Science of India, India [20] Matteson, DS; James, NA, A nonparametric approach for multiple change point analysis of multivariate data, J. Am. Stat. Assoc., 109, 505, 334-345 (2014) · Zbl 1367.62260 [21] Modisett, MC; Maboudou-Tchao, EM, Significantly lower estimates of volatility arise from the use of open-high-low-close price data, N. Am. Actuar. J., 14, 1, 68-85 (2010) [22] Nugent, C.: S&P 500 stock data. (2018) https://www.kaggle.com/camnugent/sandp500, Kaggle dataset version 4 [23] Page, ES, Continuous inspection schemes, Biometrika, 41, 1-2, 100-115 (1954) · Zbl 0056.38002 [24] R: a Language and Environment for Statistical Computing (2019), Vienna: R Foundation for Statistical Computing, Vienna [25] Scott, AJ; Knott, M., A cluster analysis method for grouping means in the analysis of variance, Biometrics, 30, 3, 507-512 (1974) · Zbl 0284.62044 [26] Terrera, GM; van den Hout, A.; Matthews, FE, Random change point models: investigating cognitive decline in the presence of missing data, J. Appl.Stat., 38, 4, 705-716 (2011) [27] Tickle, SO; Eckley, IA; Fearnhead, P.; Haynes, K., Parallelization of a common changepoint detection method, J. Comput. Gr. Stat., 0, 1-13 (2019) [28] Truong, C., Oudre, L., Vayatis, N.: Selective review of offline change point detection methods. Signal Process. 167 (2020). 10.1016/j.sigpro.2019.107299 · Zbl 07160286 [29] Vostrikova, L., Detecting ‘disorder’ in multidimensional random processes, Sov. Math. Dokl., 24, 55-59 (1981) · Zbl 0487.62072 [30] Wang, T., Samworth, R.: InspectChangepoint: high-dimensional changepoint estimation via sparse projection. CRAN R package version 1.0.1 (2016) [31] Wang, T.; Samworth, RJ, High dimensional change point estimation via sparse projection, J. R. Stat. Soc. Ser. B, 80, 1, 57-83 (2018) · Zbl 1439.62199 [32] Wickens, T., The Geometry of Multivariate Statistics (1995), Hillsdale: Lawrence Erlbaum Associates Inc., Hillsdale [33] Zhang, NR; Siegmund, DO, A modified Bayes information criterion with applications to the analysis of comparative genomic hybridization data, Biometrics, 63, 1, 22-32 (2007) · Zbl 1206.62174 [34] Zhang, NR; Siegmund, DO; Ji, H.; Li, JZ, Detecting simultaneous changepoints in multiple sequences, Biometrika, 97, 3, 631-645 (2010) [35] Zou, C.; Yin, G.; Feng, L.; Wang, Z., Nonparametric maximum likelihood approach to multiple change-point problems, Ann. Stat., 42, 3, 970-1002 (2014) · Zbl 1305.62158
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.