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Clustering of discretely observed diffusion processes

Author

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  • Alessandro De Gregorio

    (Università di Milano, Italy)

  • Stefano Iacus

    (Department of Economics, Business and Statistics, University of Milan, IT)

Abstract

In this paper a new dissimilarity measure to identify groups of assets dynamics is proposed. The underlying generating process is assumed to be a diffusion process solution of stochastic differential equations and observed at discrete time. The mesh of observations is not required to shrink to zero. As distance between two observed paths, the quadratic distance of the corresponding estimated Markov operators is considered. Analysis of both synthetic data and real financial data from NYSE/NASDAQ stocks, give evidence that this distance seems capable to catch differences in both the drift and diffusion coefficients contrary to other commonly used metrics.

Suggested Citation

  • Alessandro De Gregorio & Stefano Iacus, 2008. "Clustering of discretely observed diffusion processes," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1077, Universitá degli Studi di Milano.
    • Handle: RePEc:bep:unimip:unimi-1077
    Note: oai:cdlib1:unimi-1077
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    Cited by:

    1. 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.
    2. 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.
    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. 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.
    5. 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.

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