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Clustering of discretely observed diffusion processes. (English) Zbl 05689613
Summary: 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 \(L^{1}\) 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.

MSC:
62-08 Computational methods for problems pertaining to statistics
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62M05 Markov processes: estimation; hidden Markov models
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P05 Applications of statistics to actuarial sciences and financial mathematics
Software:
sde; dtw; R; fda (R)
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References:
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