Electronic Journal of Statistics

A wavelet-based approach for detecting changes in second order structure within nonstationary time series

R. Killick, I. A. Eckley, and P. Jonathan

Full-text: Open access

Abstract

This article proposes a test to detect changes in general autocovariance structure in nonstationary time series. Our approach is founded on the locally stationary wavelet (LSW) process model for time series which has previously been used for classification and segmentation of time series. Using this framework we form a likelihood-based hypothesis test and demonstrate its performance against existing methods on various simulated examples as well as applying it to a problem arising from ocean engineering.

Article information

Source
Electron. J. Statist., Volume 7 (2013), 1167-1183.

Dates
First available in Project Euclid: 23 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1366722164

Digital Object Identifier
doi:10.1214/13-EJS799

Mathematical Reviews number (MathSciNet)
MR3056071

Zentralblatt MATH identifier
1337.62269

Keywords
segmentation wavelets local stationarity significant wave height

Citation

Killick, R.; Eckley, I. A.; Jonathan, P. A wavelet-based approach for detecting changes in second order structure within nonstationary time series. Electron. J. Statist. 7 (2013), 1167--1183. doi:10.1214/13-EJS799. https://projecteuclid.org/euclid.ejs/1366722164


Export citation

References

  • Ahamada, I., Jouini, J., Boutahar, M., 2004. Detecting multiple breaks in time series covariance structure: a non-parametric approach based on the evolutionary spectral density. Applied Economics 36 (10), 1095–1101.
  • Bai, J., Perron, P., 2003. Computation and analysis of multiple structural change models. Journal of Applied Econometrics 18 (1), 1–22.
  • Berkes, I., Gombay, E., Horvath, L., 2009. Testing for changes in the covariance structure of linear processes. Journal of Statistical Planning and Inference 139 (6), 2044 –, 2063.
  • Chen, J., Gupta, A. K., 2000. Parametric statistical change point analysis., Birkhauser.
  • Cho, H., Fryzlewicz, P., 2012. Multiscale and multilevel technique for consistent segmentation of nonstationary time series. Statistica Sinica 22, 207–229.
  • Csorgo, M., Horváth, L., 1997. Limit theorems in change-point analysis. Wiley series in probability and statistics., Wiley.
  • Davis, R. A., Lee, T. C. M., Rodriguez-Yam, G. A., 2006. Structural break estimation for nonstationary time series models. Journal of the American Statistical Association 101 (473), 223–239.
  • Eckley, I. A., Fearnhead, P., Killick, R., 2011. Analysis of changepoint models. In: Barber, D., Cemgil, T., Chiappa, S. (Eds.), Bayesian Time Series Models. Cambridge University, Press.
  • Fryzlewicz, P., Nason, G. P., 2006. Haar-fisz estimation of evolutionary wavelet spectra. Journal of the Royal Statistical Society (Series B) 68 (4), 611–634.
  • Gombay, E., 2008. Change detection in autoregressive time series. Journal of Multivariate Analysis 99 (3), 451–464.
  • Gott, A., Eckley, I., 2013. A note on the effect of wavelet choice on the estimation of the evolutionary wavelet spectrum. Communications in statistics - simulation and computation 42, 393–406.
  • Harchaoui, Z., Levy-Leduc, C., 2010. Multiple change-point estimation with a total variation penalty. Journal of the American Statistical Association 105 (492), 1480–1493.
  • Hidgkins, G. A., James, I. C., Huntington, T. G., 2002. Historical changes in lake ice-out dates as indicators of climate change in new england, 1850–2000. International Journal Climatology 22, 1819–1827.
  • Killick, R., Eckley, I. A., 2010. changepoint: Analysis of Changepoint Models. Lancaster University, Lancaster, UK., http://CRAN.R-project.org/pacakge=changepoint
  • Killick, R., Fearnhead, P., Eckley, I. A., 2012. Optimal detection of changepoints with a linear computational cost. Journal of the American Statistical Association 107 (500), 1590–1598.
  • Lavielle, M., 2005. Using penalized contrasts for the change-point problem. Signal Processing 85, 1501–1510.
  • Nason, G. P., 2008. Wavelet Methods in Statistics with R. Springer, New, York.
  • Nason, G. P., von Sachs, R., Kroisandt, G., 2000. Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum. Journal of the Royal Statistical Society (Series B) 62 (2), 271–292.
  • Ombao, H. C., Raz, J. A., von Sachs, R., Malow, B. A., 2001. Automatic Statistical Analysis of Bivariate Nonstationary Time Series. In Memory of Jonathan A. Raz. Journal of the American Statistical Association 96 (454), 543–560.
  • Percival, D. B., Walden, A. T., 2006. Wavelet Methods for Time Series Analysis. Cambridge University, Press.
  • Schnabel, R. B., Eskow, E., 1999. A revised modified cholesky factorization algorithm. SIAM J. Optim 9, 1135–1148.
  • Scott, A. J., Knott, M., 1974. A cluster analysis method for grouping means in the analysis of variance. Biometrics 30 (3), 507–512.
  • Vostrikova, L. J., 1981. Detecting disorder in multidimensional random processes. Soviet Mathematics Doklady 24, 55–59.