1,927
Views
23
CrossRef citations to date
0
Altmetric
Theory and Methods

A Likelihood Ratio Approach to Sequential Change Point Detection for a General Class of Parameters

&
Pages 1361-1377 | Received 22 Feb 2018, Accepted 14 May 2019, Published online: 26 Jul 2019

References

  • Andrews, D. (1991), “Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation,” Econometrica, 59, 817–858. DOI: 10.2307/2938229.
  • Aue, A., Hörmann, S., Horváth, L., Hušková, M., and Steinebach, J. G. (2012), “Sequential Testing for the Stability of High-Frequency Portfolio Betas,” Econometric Theory, 28, 804–837. DOI: 10.1017/S0266466611000673.
  • Aue, A., Hörmann, S., Horváth, L., and Reimherr, M. (2009a), “Break Detection in the Covariance Structure of Multivariate Time Series Models,” The Annals of Statistics, 37, 4046–4087. DOI: 10.1214/09-AOS707.
  • Aue, A., and Horváth, L. (2013), “Structural Breaks in Time Series,” Journal of Time Series Analysis, 34, 1–16. DOI: 10.1111/j.1467-9892.2012.00819.x.
  • Aue, A., Horváth, L., Husková, M., and Kokoszka, P. (2006), “Change-Point Monitoring in Linear Models,” The Econometrics Journal, 9, 373–403. DOI: 10.1111/j.1368-423X.2006.00190.x.
  • Aue, A., Horváth, L., and Reimherr, M. L. (2009), “Delay Times of Sequential Procedures for Multiple Time Series Regression Models,” Journal of Econometrics, 149, 174–190. DOI: 10.1016/j.jeconom.2008.12.018.
  • Bahadur, R. R. (1966), “A Note on Quantiles in Large Samples,” The Annals of Mathematical Statistics, 37, 577–580. DOI: 10.1214/aoms/1177699450.
  • Chu, C.-S. J., Stinchcombe, M., and White, H. (1996), “Monitoring Structural Change,” Econometrica, 64, 1045–1065. DOI: 10.2307/2171955.
  • Csörgö, M., and Horváth, L. (1997), Limit Theorems in Change-Point Analysis, Wiley Series in Probability and Statistics, New York: Wiley.
  • 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. DOI: 10.1214/aos/1176324468.
  • Dette, H., and Wied, D. (2016), “Detecting Relevant Changes in Time Series Models,” Journal of the Royal Statistical Society, Series B, 78, 371–394. DOI: 10.1111/rssb.12121.
  • Fremdt, S. (2014), “Page’s Sequential Procedure for Change-Point Detection in Time Series Regression,” Statistics, 48, 1–28. DOI: 10.1080/02331888.2013.870568.
  • Hinkley, D. V. (1971), “Inference About the Change-Point From Cumulative Sum Tests,” Biometrika, 58, 509–523. DOI: 10.1093/biomet/58.3.509.
  • Horváth, L., Hušková, M., Kokoszka, P., and Steinebach, J. (2004), “Monitoring Changes in Linear Models,” Journal of Statistical Planning and Inference, 126, 225–251. DOI: 10.1016/j.jspi.2003.07.014.
  • Jandhyala, V., Fotopoulos, S., MacNeill, I., and Liu, P. (2013), “Inference for Single and Multiple Change-Points in Time Series,” Journal of Time Series Analysis, 34, 423–446. DOI: 10.1111/jtsa.12035.
  • Jirak, M. (2015), “Uniform Change Point Tests in High Dimension,” The Annals of Statistics, 43, 2451–2483. DOI: 10.1214/15-AOS1347.
  • Kifer, Y. (2017), “Functional Erdös-Rényi Law of Large Numbers for Nonconventional Sums Under Weak Dependence,” Electronic Journal of Probability, 22, 1–17. DOI: 10.1214/17-EJP39.
  • Kirch, C., and Weber, S. (2018), “Modified Sequential Change Point Procedures Based on Estimating Functions,” Electronic Journal of Statistics, 12, 1579–1613. DOI: 10.1214/18-EJS1431.
  • Lai, T. L. (1995), “Sequential Changepoint Detection in Quality Control and Dynamical Systems,” Journal of the Royal Statistical Society, Series B, 57, 613–658. DOI: 10.1111/j.2517-6161.1995.tb02052.x.
  • Moustakides, G. V. (1986), “Optimal Stopping Times for Detecting Changes in Distributions,” The Annals of Statistics, 14, 1379–1387. DOI: 10.1214/aos/1176350164.
  • Nikiforov, I. (1987), “Sequential Detection of Changes in Stochastic Systems,” in 2nd IFAC Workshop on Adaptive Systems in Control and Signal Processing 1986, Lund, Sweden, 30 June–2 July 1986, IFAC Proceedings Volumes, 20, 321–327. DOI: 10.1016/S1474-6670(17)55981-9.
  • Page, E. S. (1954), “Continuous Inspection Schemes,” Biometrika, 41, 100–115.
  • Pape, K., Wied, D., and Galeano, P. (2016), “Monitoring Multivariate Variance Changes,” Journal of Empirical Finance, 39, 54–68. DOI: 10.1016/j.jempfin.2016.08.007.
  • Shao, Q.-M. (1995), “On a Conjecture of Révész,” Proceedings of the American Mathematical Society, 123, 575–582. DOI: 10.2307/2160916.
  • Shao, X. (2015), “Self-Normalization for Time Series: A Review of Recent Developments,” Journal of the American Statistical Association, 110, 1797–1817. DOI: 10.1080/01621459.2015.1050493.
  • Shao, X., and Zhang, X. (2010), “Testing for Change Points in Time Series,” Journal of the American Statistical Association, 105, 1228–1240. DOI: 10.1198/jasa.2010.tm10103.
  • Wasserman, L. (2010), All of Nonparametric Statistics (1st ed.), New York: Springer Publishing Company, Inc.
  • Wied, D., and Galeano, P. (2013), “Monitoring Correlation Change in a Sequence of Random Variables,” Journal of Statistical Planning and Inference, 143, 186–196. DOI: 10.1016/j.jspi.2012.06.007.
  • Wu, W. B. (2005a), “Nonlinear System Theory: Another Look at Dependence,” Proceedings of the National Academy of Sciences of the United States of America, 102, 14150–14154. DOI: 10.1073/pnas.0506715102.
  • Wu, W. B. (2005b), “On the Bahadur Representation of Sample Quantiles for Dependent Sequences,” The Annals of Statistics, 33, 1934–1963. DOI: 10.1214/009053605000000291.
  • Zeileis, A. (2004), “Econometric Computing With HC and HAC Covariance Matrix Estimators,” Journal of Statistical Software, 11, 1–17. DOI: 10.18637/jss.v011.i10.
  • Zhang, T., and Lavitas, L. (2018), “Unsupervised Self-Normalized Change-Point Testing for Time Series,” Journal of the American Statistical Association, 113, 637–648. DOI: 10.1080/01621459.2016.1270214.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.