IDEAS home Printed from https://ideas.repec.org/p/arx/papers/0809.3902.html
   My bibliography  Save this paper

Clustering of discretely observed diffusion processes

Author

Listed:
  • Alessandro De Gregorio
  • Stefano Maria Iacus

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 Maria Iacus, 2008. "Clustering of discretely observed diffusion processes," Papers 0809.3902, arXiv.org.
    • Handle: RePEc:arx:papers:0809.3902
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/0809.3902
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Hansen, Lars Peter & Alexandre Scheinkman, Jose & Touzi, Nizar, 1998. "Spectral methods for identifying scalar diffusions," Journal of Econometrics, Elsevier, vol. 86(1), pages 1-32, June.
    2. Alonso, A.M. & Berrendero, J.R. & Hernandez, A. & Justel, A., 2006. "Time series clustering based on forecast densities," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 762-776, November.
    3. Junichi Hirukawa, 2006. "Cluster Analysis For Non-Gaussian Locally Stationary Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(01), pages 113-132.
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    5. 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.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    7. Corduas, Marcella & Piccolo, Domenico, 2008. "Time series clustering and classification by the autoregressive metric," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1860-1872, January.
    8. Gobet, Emmanuel & Hoffmann, Marc & Reiß, Markus, 2002. "Nonparametric estimation of scalar diffusions based on low frequency data is ill-posed," SFB 373 Discussion Papers 2002,57, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    9. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
    10. Otranto, Edoardo, 2008. "Clustering heteroskedastic time series by model-based procedures," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4685-4698, June.
    11. Giorgino, Toni, 2009. "Computing and Visualizing Dynamic Time Warping Alignments in R: The dtw Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 31(i07).
    12. Domenico Piccolo, 1990. "A Distance Measure For Classifying Arima Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 11(2), pages 153-164, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jianqing Fan, 2004. "A selective overview of nonparametric methods in financial econometrics," Papers math/0411034, arXiv.org.
    2. Sonia Díaz & José Vilar, 2010. "Comparing Several Parametric and Nonparametric Approaches to Time Series Clustering: A Simulation Study," Journal of Classification, Springer;The Classification Society, vol. 27(3), pages 333-362, November.
    3. Liu, Shen & Maharaj, Elizabeth Ann, 2013. "A hypothesis test using bias-adjusted AR estimators for classifying time series in small samples," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 32-49.
    4. Vilar, J.A. & Alonso, A.M. & Vilar, J.M., 2010. "Non-linear time series clustering based on non-parametric forecast densities," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2850-2865, November.
    5. Pierpaolo D’Urso & Livia Giovanni & Riccardo Massari & Dario Lallo, 2013. "Noise fuzzy clustering of time series by autoregressive metric," METRON, Springer;Sapienza Università di Roma, vol. 71(3), pages 217-243, November.
    6. E. Otranto, 2011. "Classification of Volatility in Presence of Changes in Model Parameters," Working Paper CRENoS 201113, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    7. Giovanni De Luca & Paola Zuccolotto, 2011. "A tail dependence-based dissimilarity measure for financial time series clustering," 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. 5(4), pages 323-340, December.
    8. Christian Gourieroux & Hung T. Nguyen & Songsak Sriboonchitta, 2017. "Nonparametric estimation of a scalar diffusion model from discrete time data: a survey," Annals of Operations Research, Springer, vol. 256(2), pages 203-219, September.
    9. Kristensen, Dennis, 2004. "Estimation in two classes of semiparametric diffusion models," LSE Research Online Documents on Economics 24739, London School of Economics and Political Science, LSE Library.
    10. B. Lafuente-Rego & P. D’Urso & J. A. Vilar, 2020. "Robust fuzzy clustering based on quantile autocovariances," Statistical Papers, Springer, vol. 61(6), pages 2393-2448, December.
    11. Umberto Triacca, 2016. "Measuring the Distance between Sets of ARMA Models," Econometrics, MDPI, vol. 4(3), pages 1-11, July.
    12. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    13. Geoffrey Poitras & John Heaney, 2015. "Classical Ergodicity and Modern Portfolio Theory," Post-Print hal-03680380, HAL.
    14. Antonio Mele, 2003. "Fundamental Properties of Bond Prices in Models of the Short-Term Rate," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 679-716, July.
    15. Otranto, Edoardo, 2010. "Identifying financial time series with similar dynamic conditional correlation," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 1-15, January.
    16. Yu, Jun, 2014. "Econometric Analysis Of Continuous Time Models: A Survey Of Peter Phillips’S Work And Some New Results," Econometric Theory, Cambridge University Press, vol. 30(4), pages 737-774, August.
    17. Abel Rodriguez & Enrique ter Horst, 2008. "Measuring expectations in options markets: An application to the SP500 index," Papers 0901.0033, arXiv.org.
    18. F. Fornari & A. Mele, 1998. "ARCH Models and Option Pricing : The Continuous Time Connection," THEMA Working Papers 98-30, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    19. Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
    20. Kristensen, Dennis, 2008. "Estimation of partial differential equations with applications in finance," Journal of Econometrics, Elsevier, vol. 144(2), pages 392-408, June.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:0809.3902. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.