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Time series clustering using fragmented autocorrelations

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  • Albino, Andreia
  • Caiado, Jorge
  • Crato, Nuno

Abstract

We propose and study an autocorrelation procedure designed to characterize and compare large sets of long time series. This time-domain procedure is contrasted with a frequency-domain approach that has recently been introduced and discussed in the literature. In both cases, instead of using all the information available from data, which would be computationally very expensive, adequate regularization rules select and summarize the most relevant information suitable for clustering purposes. Essentially, we suggest to use the autocorrelation coefficients of the time series that are only computed around the lags of greatest interest. Then, we study this method in several ways. We argue theoretically that fragmenting the autocorrelation function can have efficiency advantages when comparing time series. By means of a large simulation study, we show that the suggested procedure can condense the relevant information of the time series. We compare its results with those from the frequency domain counterpart. We further illustrate this procedure in a study of the evolution of several stock markets indices and show the effect of recent financial crises on the behaviour of these indices.

Suggested Citation

  • Albino, Andreia & Caiado, Jorge & Crato, Nuno, 2024. "Time series clustering using fragmented autocorrelations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 650(C).
    • Handle: RePEc:eee:phsmap:v:650:y:2024:i:c:s0378437124004904
    DOI: 10.1016/j.physa.2024.129981
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    References listed on IDEAS

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    1. Jorge Caiado & Nuno Crato, 2010. "Identifying common dynamic features in stock returns," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 797-807.
    2. Caiado, Jorge & Crato, Nuno & Pena, Daniel, 2006. "A periodogram-based metric for time series classification," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2668-2684, June.
    3. Jorge Caiado & Nuno Crato & Pilar Poncela, 2020. "A fragmented-periodogram approach for clustering big data time series," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(1), pages 117-146, March.
    4. Otranto, Edoardo, 2008. "Clustering heteroskedastic time series by model-based procedures," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4685-4698, June.
    5. Domenico Piccolo, 1990. "A Distance Measure For Classifying Arima Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 11(2), pages 153-164, March.
    6. Caiado, Jorge & Crato, Nuno & Peña, Daniel, 2009. "Comparison of time series with unequal length in the frequency domain," MPRA Paper 15310, University Library of Munich, Germany.
    7. João A. Bastos & Jorge Caiado, 2014. "Clustering financial time series with variance ratio statistics," Quantitative Finance, Taylor & Francis Journals, vol. 14(12), pages 2121-2133, December.
    8. Lúcio, Francisco & Caiado, Jorge, 2022. "COVID-19 and Stock Market Volatility: A Clustering Approach for S&P 500 Industry Indices," Finance Research Letters, Elsevier, vol. 49(C).
    Full references (including those not matched with items on IDEAS)

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