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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.

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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 54 (2010)
Issue (Month): 2 (February)
Pages: 598-606

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Handle: RePEc:eee:csdana:v:54:y:2010:i:2:p:598-606

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  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.
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  5. 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.
  6. E. Otranto, 2008. "Clustering Heteroskedastic Time Series by Model-Based Procedures," Working Paper CRENoS 200801, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
  7. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  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. 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.
  10. 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.
  11. 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.
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