IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i8p817-d532936.html
   My bibliography  Save this article

Statistical Tests of Symbolic Dynamics

Author

Listed:
  • Fernando López

    (Departamento de Métodos Cuantitativos, Universidad Politécnica de Cartagena, 30202 Cartagena, Spain
    These authors contributed equally to this work.)

  • Mariano Matilla-García

    (Departamento de Economía Aplicada y Estadística, Universidad Nacional de Educación a Distancia (UNED), 28040 Madrid, Spain
    These authors contributed equally to this work.)

  • Jesús Mur

    (Departamento de Análisis Económico, Universidad de Zaragoza, 50018 Zaragoza, Spain
    These authors contributed equally to this work.)

  • Manuel Ruiz Marín

    (Departamento de Métodos Cuantitativos, Universidad Politécnica de Cartagena, 30202 Cartagena, Spain
    These authors contributed equally to this work.)

Abstract

A novel general method for constructing nonparametric hypotheses tests based on the field of symbolic analysis is introduced in this paper. Several existing tests based on symbolic entropy that have been used for testing central hypotheses in several branches of science (particularly in economics and statistics) are particular cases of this general approach. This family of symbolic tests uses few assumptions, which increases the general applicability of any symbolic-based test. Additionally, as a theoretical application of this method, we construct and put forward four new statistics to test for the null hypothesis of spatiotemporal independence. There are very few tests in the specialized literature in this regard. The new tests were evaluated with the mean of several Monte Carlo experiments. The results highlight the outstanding performance of the proposed test.

Suggested Citation

  • Fernando López & Mariano Matilla-García & Jesús Mur & Manuel Ruiz Marín, 2021. "Statistical Tests of Symbolic Dynamics," Mathematics, MDPI, vol. 9(8), pages 1-21, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:817-:d:532936
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/8/817/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/8/817/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lunde A. & Timmermann A., 2004. "Duration Dependence in Stock Prices: An Analysis of Bull and Bear Markets," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 253-273, July.
    2. Peter M Robinson, 2009. "Large-Sample Inference on SpatialDependence," STICERD - Econometrics Paper Series 533, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. Craig Brett & Joris Pinkse, 1997. "Those Taxes are all over the Map! A Test for Spatial Independence of Municipal Tax Rates in British Columbia," International Regional Science Review, , vol. 20(1-2), pages 131-151, April.
    4. P. M. Robinson, 2009. "Large-sample inference on spatial dependence," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 68-82, January.
    5. M. Victoria Caballero-Pintado & Mariano Matilla-García & Manuel Ruiz Marín, 2019. "Symbolic correlation integral," Econometric Reviews, Taylor & Francis Journals, vol. 38(5), pages 533-556, May.
    6. López, Fernando & Matilla-García, Mariano & Mur, Jesús & Marín, Manuel Ruiz, 2010. "A non-parametric spatial independence test using symbolic entropy," Regional Science and Urban Economics, Elsevier, vol. 40(2-3), pages 106-115, May.
    7. Alexander Schnurr & Herold Dehling, 2017. "Testing for Structural Breaks via Ordinal Pattern Dependence," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 706-720, April.
    8. Matilla-Garci­a, Mariano & Ruiz Mari­n, Manuel, 2008. "A non-parametric independence test using permutation entropy," Journal of Econometrics, Elsevier, vol. 144(1), pages 139-155, May.
    9. Chstoph Bandt & Faten Shiha, 2007. "Order Patterns in Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(5), pages 646-665, September.
    10. Matilla-García, Mariano & Marín, Manuel Ruiz, 2010. "A new test for chaos and determinism based on symbolic dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 600-614, December.
    11. Sinn, Mathieu & Keller, Karsten, 2011. "Estimation of ordinal pattern probabilities in Gaussian processes with stationary increments," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1781-1790, April.
    12. Jose A. García-Córdoba & Mariano Matilla-García & Manuel Ruiz Marín, 2019. "A test for deterministic dynamics in spatial processes," Spatial Economic Analysis, Taylor & Francis Journals, vol. 14(3), pages 361-377, July.
    13. Yongmiao Hong & Halbert White, 2005. "Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence," Econometrica, Econometric Society, vol. 73(3), pages 837-901, May.
    14. Fernando A. López & Mariano Matilla‐García & Jesús Mur & Manuel Ruiz Marín, 2011. "Four tests of independence in spatiotemporal data," Papers in Regional Science, Wiley Blackwell, vol. 90(3), pages 663-685, August.
    15. Alexander Schnurr, 2014. "An ordinal pattern approach to detect and to model leverage effects and dependence structures between financial time series," Statistical Papers, Springer, vol. 55(4), pages 919-931, November.
    16. Matilla-Garcia, Mariano, 2007. "A non-parametric test for independence based on symbolic dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 31(12), pages 3889-3903, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Schnurr, Alexander & Fischer, Svenja, 2022. "Generalized ordinal patterns allowing for ties and their applications in hydrology," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    2. Weiß, Christian H. & Ruiz Marín, Manuel & Keller, Karsten & Matilla-García, Mariano, 2022. "Non-parametric analysis of serial dependence in time series using ordinal patterns," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    3. Christoph Bandt, 2019. "Order patterns, their variation and change points in financial time series and Brownian motion," Papers 1910.09978, arXiv.org.
    4. Betken, Annika & Dehling, Herold & Nüßgen, Ines & Schnurr, Alexander, 2021. "Ordinal pattern dependence as a multivariate dependence measure," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    5. Christoph Bandt, 2020. "Order patterns, their variation and change points in financial time series and Brownian motion," Statistical Papers, Springer, vol. 61(4), pages 1565-1588, August.
    6. Annika Betken & Jannis Buchsteiner & Herold Dehling & Ines Münker & Alexander Schnurr & Jeannette H.C. Woerner, 2021. "Ordinal patterns in long‐range dependent time series," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 969-1000, September.
    7. Giuseppe Arbia, 2011. "A Lustrum of SEA: Recent Research Trends Following the Creation of the Spatial Econometrics Association (2007--2011)," Spatial Economic Analysis, Taylor & Francis Journals, vol. 6(4), pages 377-395, July.
    8. Miguel Henry & George Judge, 2019. "Permutation Entropy and Information Recovery in Nonlinear Dynamic Economic Time Series," Econometrics, MDPI, vol. 7(1), pages 1-16, March.
    9. Elsinger, Helmut, 2013. "Comment on: A non-parametric spatial independence test using symbolic entropy," Regional Science and Urban Economics, Elsevier, vol. 43(5), pages 838-840.
    10. Herrera Gómez, Marcos & Ruiz Marín, Manuel & Mur Lacambra, Jesús & Paelinck, Jean, 2010. "A Non-Parametric Approach to Spatial Causality," MPRA Paper 36768, University Library of Munich, Germany.
    11. López-Hernández , Fernando A. & Artal-Tur, Andrés & Maté-Sánchez-Val, M. Luz, 2011. "Identifying nonlinear spatial dependence patterns by using non-parametric tests: Evidence for the European Union," INVESTIGACIONES REGIONALES - Journal of REGIONAL RESEARCH, Asociación Española de Ciencia Regional, issue 21, pages 19-36.
    12. Herrera Gómez, Marcos, 2010. "Causalidad Espacial. Enfoque No Paramétrico [Spatial Causality. Non-Parametric Approach]," MPRA Paper 61326, University Library of Munich, Germany.
    13. Herrera Gómez, Marcos & Ruiz Marín, Manuel & Mur Lacambra, Jesús, 2011. "Detección de Dependencia Espacial mediante Análisis Simbólico [Detection of Spatial Dependence using Symbolic Analysis]," MPRA Paper 38603, University Library of Munich, Germany.
    14. López, Fernando & Matilla-García, Mariano & Mur, Jesús & Marín, Manuel Ruiz, 2010. "A non-parametric spatial independence test using symbolic entropy," Regional Science and Urban Economics, Elsevier, vol. 40(2-3), pages 106-115, May.
    15. Joris Pinkse & Margaret E. Slade, 2010. "The Future Of Spatial Econometrics," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 103-117, February.
    16. Herrera Gómez, Marcos & Ruiz Marín, Manuel & Mur Lacambra, Jesús, 2014. "Testing Spatial Causality in Cross-section Data," MPRA Paper 56678, University Library of Munich, Germany.
    17. Alexander Schnurr, 2015. "An Ordinal Pattern Approach to Detect and to Model Leverage Effects and Dependence Structures Between Financial Time Series," Papers 1502.07321, arXiv.org.
    18. Herrera Gómez, Marcos & Mur Lacambra, Jesús & Ruiz Marín, Manuel, 2012. "Selecting the Most Adequate Spatial Weighting Matrix:A Study on Criteria," MPRA Paper 73700, University Library of Munich, Germany.
    19. Richard Harris & John Moffat & Victoria Kravtsova, 2011. "In Search of ‘ W ’," Spatial Economic Analysis, Taylor & Francis Journals, vol. 6(3), pages 249-270, February.
    20. Helmut Elsinger, 2010. "Independence Tests based on Symbolic Dynamics," Working Papers 165, Oesterreichische Nationalbank (Austrian Central Bank).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:817-:d:532936. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.