# Missing ordinal patterns in correlated noises

Recent research aiming at the distinction between deterministic or stochastic behavior in observational time series has looked into the properties of the "ordinal patterns" [C. Bandt, B. Pompe, Phys. Rev. Lett. 88 (2002) 174102]. In particular, new insight has been obtained considering the...

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todo:paper_03784371_v389_n10_p2020_Carpi2023-10-03T15:32:55Z Missing ordinal patterns in correlated noises Carpi, L.C. Saco, P.M. Rosso, O.A. Fluctuation phenomena Noise Noise and Brownian motion Random processes Time series analysis Brownian motion Correlated noise Correlation structure Decay rate Fluctuation phenomena Fractional Brownian motion Fractional Gaussian noise Noise Noise and Brownian motion One dimensional map Ordinal pattern Stochastic behavior Stochastic process White Gaussian Noise Brownian movement Decay (organic) Gaussian noise (electronic) Stochastic systems Time and motion study Time series White noise Time series analysis Recent research aiming at the distinction between deterministic or stochastic behavior in observational time series has looked into the properties of the "ordinal patterns" [C. Bandt, B. Pompe, Phys. Rev. Lett. 88 (2002) 174102]. In particular, new insight has been obtained considering the emergence of the so-called "forbidden ordinal patterns" [J.M. Amigó, S. Zambrano, M.A. F Sanjuán, Europhys. Lett. 79 (2007) 50001]. It was shown that deterministic one-dimensional maps always have forbidden ordinal patterns, in contrast with time series generated by an unconstrained stochastic process in which all the patterns appear with probability one. Techniques based on the comparison of this property in an observational time series and in white Gaussian noise were implemented. However, the comparison with correlated stochastic processes was not considered. In this paper we used the concept of "missing ordinal patterns" to study their decay rate as a function of the time series length in three stochastic processes with different degrees of correlation: fractional Brownian motion, fractional Gaussian noise and, noises with f- k power spectrum. We show that the decay rate of "missing ordinal patterns" in these processes depend on their correlation structures. We finally discuss the implications of the present results for the use of these properties as a tool for distinguishing deterministic from stochastic processes. © 2010 Elsevier B.V. All rights reserved. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03784371_v389_n10_p2020_Carpi |

institution |
Universidad de Buenos Aires |

institution_str |
I-28 |

repository_str |
R-134 |

collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |

topic |
Fluctuation phenomena Noise Noise and Brownian motion Random processes Time series analysis Brownian motion Correlated noise Correlation structure Decay rate Fluctuation phenomena Fractional Brownian motion Fractional Gaussian noise Noise Noise and Brownian motion One dimensional map Ordinal pattern Stochastic behavior Stochastic process White Gaussian Noise Brownian movement Decay (organic) Gaussian noise (electronic) Stochastic systems Time and motion study Time series White noise Time series analysis |

spellingShingle |
Fluctuation phenomena Noise Noise and Brownian motion Random processes Time series analysis Brownian motion Correlated noise Correlation structure Decay rate Fluctuation phenomena Fractional Brownian motion Fractional Gaussian noise Noise Noise and Brownian motion One dimensional map Ordinal pattern Stochastic behavior Stochastic process White Gaussian Noise Brownian movement Decay (organic) Gaussian noise (electronic) Stochastic systems Time and motion study Time series White noise Time series analysis Carpi, L.C. Saco, P.M. Rosso, O.A. Missing ordinal patterns in correlated noises |

topic_facet |
Fluctuation phenomena Noise Noise and Brownian motion Random processes Time series analysis Brownian motion Correlated noise Correlation structure Decay rate Fluctuation phenomena Fractional Brownian motion Fractional Gaussian noise Noise Noise and Brownian motion One dimensional map Ordinal pattern Stochastic behavior Stochastic process White Gaussian Noise Brownian movement Decay (organic) Gaussian noise (electronic) Stochastic systems Time and motion study Time series White noise Time series analysis |

description |
Recent research aiming at the distinction between deterministic or stochastic behavior in observational time series has looked into the properties of the "ordinal patterns" [C. Bandt, B. Pompe, Phys. Rev. Lett. 88 (2002) 174102]. In particular, new insight has been obtained considering the emergence of the so-called "forbidden ordinal patterns" [J.M. Amigó, S. Zambrano, M.A. F Sanjuán, Europhys. Lett. 79 (2007) 50001]. It was shown that deterministic one-dimensional maps always have forbidden ordinal patterns, in contrast with time series generated by an unconstrained stochastic process in which all the patterns appear with probability one. Techniques based on the comparison of this property in an observational time series and in white Gaussian noise were implemented. However, the comparison with correlated stochastic processes was not considered. In this paper we used the concept of "missing ordinal patterns" to study their decay rate as a function of the time series length in three stochastic processes with different degrees of correlation: fractional Brownian motion, fractional Gaussian noise and, noises with f- k power spectrum. We show that the decay rate of "missing ordinal patterns" in these processes depend on their correlation structures. We finally discuss the implications of the present results for the use of these properties as a tool for distinguishing deterministic from stochastic processes. © 2010 Elsevier B.V. All rights reserved. |

format |
JOUR |

author |
Carpi, L.C. Saco, P.M. Rosso, O.A. |

author_facet |
Carpi, L.C. Saco, P.M. Rosso, O.A. |

author_sort |
Carpi, L.C. |

title |
Missing ordinal patterns in correlated noises |

title_short |
Missing ordinal patterns in correlated noises |

title_full |
Missing ordinal patterns in correlated noises |

title_fullStr |
Missing ordinal patterns in correlated noises |

title_full_unstemmed |
Missing ordinal patterns in correlated noises |

title_sort |
missing ordinal patterns in correlated noises |

url |
http://hdl.handle.net/20.500.12110/paper_03784371_v389_n10_p2020_Carpi |

work_keys_str_mv |
AT carpilc missingordinalpatternsincorrelatednoises AT sacopm missingordinalpatternsincorrelatednoises AT rossooa missingordinalpatternsincorrelatednoises |

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1782029896260780032 |