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Clustering of discretely observed diffusion processes

  • Alessandro De Gregorio

    (Università di Milano, Italy)

  • Stefano Iacus

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

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.

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Paper provided by Universitá degli Studi di Milano in its series UNIMI - Research Papers in Economics, Business, and Statistics with number unimi-1077.

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Date of creation: 18 Sep 2008
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Handle: RePEc:bep:unimip:unimi-1077
Note: oai:cdlib1:unimi-1077
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  1. Otranto, Edoardo, 2008. "Clustering heteroskedastic time series by model-based procedures," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4685-4698, June.
  2. 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.
  3. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-60, May.
  4. 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 637-54, May-June.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. Toni Giorgino, . "Computing and Visualizing Dynamic Time Warping Alignments in R: The dtw Package," Journal of Statistical Software, American Statistical Association, vol. 31(i07).
  10. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  11. 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.
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