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Trend of high dimensional time series estimation using low-rank matrix factorization: heuristics and numerical experiments via the TrendTM package

Author

Listed:
  • Emilie Lebarbier

    (Univ. Paris Nanterre)

  • Nicolas Marie

    (Univ. Paris Nanterre)

  • Amélie Rosier

    (Univ. Paris Nanterre
    ESME Sudria)

Abstract

This article focuses on the practical issue of a recent theoretical method proposed for trend estimation in high dimensional time series. This method falls within the scope of the low-rank matrix factorization methods in which the temporal structure is taken into account. It consists of minimizing a penalized criterion, theoretically efficient but which depends on two constants to be chosen in practice. We propose a two-step strategy to solve this question based on two different known heuristics. The performance and a comparison of the strategies are studied through an important simulation study in various scenarios. In order to make the estimation method with the best strategy available to the community, we implemented the method in an R package TrendTM which is presented and used here. Finally, we give a geometric interpretation of the results by linking it to PCA and use the results to solve a high-dimensional curve clustering problem. The package is available on CRAN.

Suggested Citation

  • Emilie Lebarbier & Nicolas Marie & Amélie Rosier, 2025. "Trend of high dimensional time series estimation using low-rank matrix factorization: heuristics and numerical experiments via the TrendTM package," Computational Statistics, Springer, vol. 40(2), pages 1097-1122, February.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:2:d:10.1007_s00180-024-01519-9
    DOI: 10.1007/s00180-024-01519-9
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    References listed on IDEAS

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    1. Julien Jacques & Cristian Preda, 2014. "Functional data clustering: a survey," 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. 8(3), pages 231-255, September.
    2. Xavier Collilieux & Emilie Lebarbier & Stéphane Robin, 2019. "A factor model approach for the joint segmentation with between‐series correlation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(3), pages 686-705, September.
    3. Zhaoxing Gao & Ruey S. Tsay, 2022. "Modeling High-Dimensional Time Series: A Factor Model With Dynamically Dependent Factors and Diverging Eigenvalues," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(539), pages 1398-1414, September.
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