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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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    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. 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.
    4. Lasse Holmström & Leena Pasanen, 2017. "Statistical Scale Space Methods," International Statistical Review, International Statistical Institute, vol. 85(1), pages 1-30, April.

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