Persona:
Matilla García, Mariano

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ORCID
0000-0002-6007-3522
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Matilla García
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Mariano
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2019 - 201912020 - 20222
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Autor: Ruiz Marín, Manuel × search.filters.applied.f.itemDepartamento: Economía Aplicada y Estadística ×

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Mostrando 1 - 3 de 3
  • Miniatura
    Publicación
    Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction via Symbolic Dynamics
    (MDPI, 2021-02-11) Matilla García, Mariano; Morales, Isidro; Rodríguez, José Miguel; Ruiz Marín, Manuel
    The modeling and prediction of chaotic time series require proper reconstruction of the state space from the available data in order to successfully estimate invariant properties of the embedded attractor. Thus, one must choose appropriate time delay 𝜏∗ and embedding dimension p for phase space reconstruction. The value of 𝜏∗ can be estimated from the Mutual Information, but this method is rather cumbersome computationally. Additionally, some researchers have recommended that 𝜏∗ should be chosen to be dependent on the embedding dimension p by means of an appropriate value for the time delay 𝜏𝑤=(𝑝−1)𝜏∗, which is the optimal time delay for independence of the time series. The C-C method, based on Correlation Integral, is a method simpler than Mutual Information and has been proposed to select optimally 𝜏𝑤 and 𝜏∗. In this paper, we suggest a simple method for estimating 𝜏∗ and 𝜏𝑤 based on symbolic analysis and symbolic entropy. As in the C-C method, 𝜏∗ is estimated as the first local optimal time delay and 𝜏𝑤 as the time delay for independence of the time series. The method is applied to several chaotic time series that are the base of comparison for several techniques. The numerical simulations for these systems verify that the proposed symbolic-based method is useful for practitioners and, according to the studied models, has a better performance than the C-C method for the choice of the time delay and embedding dimension. In addition, the method is applied to EEG data in order to study and compare some dynamic characteristics of brain activity under epileptic episodes
  • Miniatura
    Publicación
    A test for deterministic dynamics in spatial processes
    (2019-01-19) García-Córdoba, Jose A.; Matilla García, Mariano; Ruiz Marín, Manuel
    We propose a statistical procedure to determine if a spatial structure that is observed in the data is generated by a deterministic (even chaotic) spatial process, rather than by a stochastic process. This procedure can be used as a specification test. It is robust against nonlinearity and nonstationarity and can complete the toolbox for testing diagnosis as well. The advantages of the presented methods are high power, simplicity, and ease and ample applicability for tests to be conducted, provided that weak conditions are required. Herein, we conduct several simulations to evaluate the performance of our procedure on well-known spatial processes and in situations where standard tests for spatial autocorrelation fail to detect spatial dependence. Guidelines for using the technique are also provided herein.
  • Miniatura
    Publicación
    Non-parametric analysis of serial dependence in time series using ordinal patterns
    (Elsevier, 2022-04) Weiß, Christian H.; Ruiz Marín, Manuel; Keller, Karsten; Matilla García, Mariano
    A list of new tests for serial dependence based on ordinal patterns are provided. These new methods rely exclusively on the order structure of the data sets. Hence, the novel tests are stable under monotone transformations of the time series and robust against small perturbations or measurement errors. The standard asymptotic distributions are given, and their finite sample behavior under linear and non-linear departures from the null of independence are studied. Moreover, it is proved that under mild conditions, any ordinal-pattern-based test is nuisance free, which is appealing for modelling, as these tests can eventually be used as misspecification tests. This property is also analyzed for finite samples and illustrated through an empirical application. Much of the discussion is based on a detailed combinatorial analysis of ordinal pattern probabilities