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Multiscale spectral analysis for detecting short and long range change points in time series

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  • Olsen, Lena Ringstad
  • Chaudhuri, Probal
  • Godtliebsen, Fred

Abstract

Identifying short and long range change points in an observed time series that consists of stationary segments is a common problem. These change points mark the time boundaries of the segments where the time series leaves one stationary state and enters another. Due to certain technical advantages, analysis is carried out in the frequency domain to identify such change points in the time domain. What is considered as a change may depend on the time scale. The results of the analysis are displayed in the form of graphs that display change points on different time horizons (time scales), which are observed to be statistically significant. The methodology is illustrated using several simulated and real time series data. The method works well to detect change points and illustrates the importance of analysing the time series on different time horizons.

Suggested Citation

  • Olsen, Lena Ringstad & Chaudhuri, Probal & Godtliebsen, Fred, 2008. "Multiscale spectral analysis for detecting short and long range change points in time series," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3310-3330, March.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:7:p:3310-3330
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    1. Hernando Ombao & Jonathan Raz & Rainer von Sachs & Wensheng Guo, 2002. "The SLEX Model of a Non-Stationary Random Process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(1), pages 171-200, March.
    2. Davis, Richard A. & Lee, Thomas C.M. & Rodriguez-Yam, Gabriel A., 2006. "Structural Break Estimation for Nonstationary Time Series Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 223-239, March.
    3. Sato, Joao R. & Morettin, Pedro A. & Arantes, Paula R. & Amaro Jr., Edson, 2007. "Wavelet based time-varying vector autoregressive modelling," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5847-5866, August.
    4. Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 551-563, November.
    5. Bruce E. Hansen, 2001. "The New Econometrics of Structural Change: Dating Breaks in U.S. Labour Productivity," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 117-128, Fall.
    6. Ombao H. C & Raz J. A & von Sachs R. & Malow B. A, 2001. "Automatic Statistical Analysis of Bivariate Nonstationary Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 543-560, June.
    7. Park, Cheolwoo & Godtliebsen, Fred & Taqqu, Murad & Stoev, Stilian & Marron, J.S., 2007. "Visualization and inference based on wavelet coefficients, SiZer and SiNos," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5994-6012, August.
    8. Polansky, Alan M., 2007. "Detecting change-points in Markov chains," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6013-6026, August.
    9. Ligges, Uwe & Weihs, Claus & Hasse-Becker, Petra, 2002. "Detection of locally stationary segments in time series: Algorithms and applications," Technical Reports 2002,11, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    10. Dahlhaus, Rainer & Neumann, Michael H., 2001. "Locally adaptive fitting of semiparametric models to nonstationary time series," Stochastic Processes and their Applications, Elsevier, vol. 91(2), pages 277-308, February.
    11. Balke, Nathan S, 1993. "Detecting Level Shifts in Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 81-92, January.
    12. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    13. Oigard, Tor Arne & Rue, Havard & Godtliebsen, Fred, 2006. "Bayesian multiscale analysis for time series data," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1719-1730, December.
    14. Cheolwoo Park & J. S. Marron & Vitaliana Rondonotti, 2004. "Dependent SiZer: Goodness-of-Fit Tests for Time Series Models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(8), pages 999-1017.
    15. Hsiao-Yun Huang & Hernando Ombao & David S. Stoffer, 2004. "Discrimination and Classification of Nonstationary Time Series Using the SLEX Model," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 763-774, January.
    16. D. S. Coates & P. J. Diggle, 1986. "Tests For Comparing Two Estimated Spectral Densities," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(1), pages 7-20, January.
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    2. Caporale, Guglielmo Maria & Gil-Alana, Luis A., 2008. "Modelling the US, UK and Japanese unemployment rates: Fractional integration and structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4998-5013, July.
    3. Lasse Holmström & Leena Pasanen, 2017. "Statistical Scale Space Methods," International Statistical Review, International Statistical Institute, vol. 85(1), pages 1-30, April.
    4. Alessandra Micheletti & Giacomo Aletti & Giulia Ferrandi & Danilo Bertoni & Daniele Cavicchioli & Roberto Pretolani, 2020. "A weighted $$\chi ^2$$ χ 2 test to detect the presence of a major change point in non-stationary Markov chains," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(4), pages 899-912, December.

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