Symbolic time-series analysis is used for estimating the parameters of chaotic systems. It is assumed that a "target model" (i.e., a discrete- or continuous-time description of the data-generating mechanism) is available, but with unknown parameters. A time series, i.e., a noisy, finite sequence of a measured (output) variable, is given. The proposed method first prescribes to symbolize the time series, i.e., to transform it into a sequence of symbols, from which the statistics of symbols are readily derived. Then, a symbolic model (in the form of a Markov chain) is derived from the data. It allows one to predict, in a probabilistic fashion, the time evolution of the symbol sequence. The unknown parameters are derived by matching either the statistics of symbols, or the symbolic prediction derived from data, with those generated by the (parametrized) target model. Three examples of application (the Henon map, a population model, and the Duffing system) prove that satisfactory results can be obtained even with short time series.

On parameter estimation of chaotic systems via symbolic time series analysis

PICCARDI, CARLO
2006-01-01

Abstract

Symbolic time-series analysis is used for estimating the parameters of chaotic systems. It is assumed that a "target model" (i.e., a discrete- or continuous-time description of the data-generating mechanism) is available, but with unknown parameters. A time series, i.e., a noisy, finite sequence of a measured (output) variable, is given. The proposed method first prescribes to symbolize the time series, i.e., to transform it into a sequence of symbols, from which the statistics of symbols are readily derived. Then, a symbolic model (in the form of a Markov chain) is derived from the data. It allows one to predict, in a probabilistic fashion, the time evolution of the symbol sequence. The unknown parameters are derived by matching either the statistics of symbols, or the symbolic prediction derived from data, with those generated by the (parametrized) target model. Three examples of application (the Henon map, a population model, and the Duffing system) prove that satisfactory results can be obtained even with short time series.
2006
File in questo prodotto:
File Dimensione Formato  
c2.pdf

Accesso riservato

: Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione 331.29 kB
Formato Adobe PDF
331.29 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/266100
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 19
  • ???jsp.display-item.citation.isi??? 18
social impact