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Clustering of discretely observed diffusion processes

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  • De Gregorio, Alessandro
  • Maria Iacus, Stefano

Abstract

A new distance to classify time series is proposed. The underlying generating process is assumed to be a diffusion process solution to stochastic differential equations and observed at discrete times. The mesh of observations is not required to shrink to zero. The new dissimilarity measure is based on the L1 distance between the Markov operators estimated on two observed paths. Simulation experiments are used to analyze the performance of the proposed distance under several conditions including perturbation and misspecification. As an example, real financial data from NYSE/NASDAQ stocks are analyzed and evidence is provided that the new distance seems capable to catch differences in both the drift and diffusion coefficients better than other commonly used non-parametric distances. Corresponding software is available in the add-on package sde for the R statistical environment.

Suggested Citation

  • De Gregorio, Alessandro & Maria Iacus, Stefano, 2010. "Clustering of discretely observed diffusion processes," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 598-606, February.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:2:p:598-606
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    1. Pierpaolo D’Urso & Livia Giovanni & Riccardo Massari, 2021. "Trimmed fuzzy clustering of financial time series based on dynamic time warping," Annals of Operations Research, Springer, vol. 299(1), pages 1379-1395, April.
    2. D’Amato, Valeria & Di Lorenzo, Emilia & Haberman, Steven & Sagoo, Pretty & Sibillo, Marilena, 2018. "De-risking strategy: Longevity spread buy-in," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 124-136.
    3. Stefano Maria Iacus & Giuseppe Porro, 2014. "Does European Monetary Union make inflation dynamics more uniform?," Applied Economics Letters, Taylor & Francis Journals, vol. 21(6), pages 391-396, April.
    4. A. Gregorio & S. M. Iacus, 2019. "Empirical $$L^2$$ L 2 -distance test statistics for ergodic diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 22(2), pages 233-261, July.
    5. 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.

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