IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v60y2019i3d10.1007_s00362-016-0845-9.html
   My bibliography  Save this article

A Gini-based time series analysis and test for reversibility

Author

Listed:
  • Amit Shelef

    (D.N. Hof Ashkelon)

  • Edna Schechtman

    (Ben-Gurion University of the Negev)

Abstract

Time reversibility is a fundamental hypothesis in time series. In this paper, Gini-based equivalents for time series concepts that enable to construct a Gini-based test for time reversibility under merely first-order moment assumptions are developed. The key idea is that the relationship between two variables using Gini (as measured by Gini autocorrelations and partial autocorrelations) can be measured in two directions, which are not necessarily equal. This implies a built-in capability to discriminate between looking at forward and backward directions in time series. The Gini creates two bi-directional Gini autocorrelations (and partial autocorrelations), looking forward and backward in time, which are not necessarily equal. The difference between them may assist in identifying models with underlying heavy-tailed and non-normal innovations. Gini-based test and Gini-based correlograms, which serve as visual tools to examine departures from the symmetry assumption, are constructed. Simulations are used to illustrate the suggested Gini-based framework and to validate the statistical test. An application to a real data set is presented.

Suggested Citation

  • Amit Shelef & Edna Schechtman, 2019. "A Gini-based time series analysis and test for reversibility," Statistical Papers, Springer, vol. 60(3), pages 687-716, June.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:3:d:10.1007_s00362-016-0845-9
    DOI: 10.1007/s00362-016-0845-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-016-0845-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-016-0845-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521770415.
    2. Schechtman, Edna & Yitzhaki, Shlomo & Artsev, Yevgeny, 2008. "Who Does Not Respond in the Household Expenditure Survey," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 329-344.
    3. Schechtman, E. & Yitzhaki, S., 1999. "On the proper bounds of the Gini correlation," Economics Letters, Elsevier, vol. 63(2), pages 133-138, May.
    4. Wodon, Quentin & Yitzhaki, Shlomo, 2006. "Convergence forward and backward?," Economics Letters, Elsevier, vol. 92(1), pages 47-51, July.
    5. Chen, Yi-Ting & Chou, Ray Y. & Kuan, Chung-Ming, 2000. "Testing time reversibility without moment restrictions," Journal of Econometrics, Elsevier, vol. 95(1), pages 199-218, March.
    6. Ramsey, James B & Rothman, Philip, 1996. "Time Irreversibility and Business Cycle Asymmetry," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 28(1), pages 1-21, February.
    7. Marcel Carcea & Robert Serfling, 2015. "A Gini Autocovariance Function for Time Series Modelling," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(6), pages 817-838, November.
    8. Shlomo Yitzhaki, 2003. "Gini’s Mean difference: a superior measure of variability for non-normal distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 285-316.
    9. Lerman, Robert I. & Yitzhaki, Shlomo, 1984. "A note on the calculation and interpretation of the Gini index," Economics Letters, Elsevier, vol. 15(3-4), pages 363-368.
    10. Vygantas Paulaauskas & Svetlozar Rachev, 2003. "Maximum likelihood estimators in regression models with infinite variance innovations," Statistical Papers, Springer, vol. 44(1), pages 47-65, January.
    11. Serfling, Robert & Xiao, Peng, 2007. "A contribution to multivariate L-moments: L-comoment matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1765-1781, October.
    12. Andrews, Beth & Davis, Richard A., 2013. "Model identification for infinite variance autoregressive processes," Journal of Econometrics, Elsevier, vol. 172(2), pages 222-234.
    13. Davis, Richard & Resnick, Sidney, 1985. "More limit theory for the sample correlation function of moving averages," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 257-279, September.
    14. Rubinstein, Mark E., 1973. "The Fundamental Theorem of Parameter-Preference Security Valuation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 8(1), pages 61-69, January.
    15. Corrado Gini, 2005. "On the measurement of concentration and variability of characters," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 1-38.
    16. Zacharias Psaradakis, 2008. "Assessing Time‐Reversibility Under Minimal Assumptions," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 881-905, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. N. V. Gribkova & J. Su & R. Zitikis, 2022. "Empirical tail conditional allocation and its consistency under minimal assumptions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 713-735, August.
    2. Wang, Zhuo & Shang, Pengjian, 2023. "Generalized distance component method based on spatial amplitude and trend difference weighting operator for complex time series," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    3. Sudheesh K. Kattumannil & N. Sreelakshmi & N. Balakrishnan, 2022. "Non-Parametric Inference for Gini Covariance and its Variants," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 790-807, August.

    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. Shelef, Amit, 2016. "A Gini-based unit root test," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 763-772.
    2. Xin Dang & Hailin Sang & Lauren Weatherall, 2019. "Gini covariance matrix and its affine equivariant version," Statistical Papers, Springer, vol. 60(3), pages 641-666, June.
    3. Serfling, Robert & Xiao, Peng, 2007. "A contribution to multivariate L-moments: L-comoment matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1765-1781, October.
    4. Yoel Finkel & Yevgeny Artsev & Shlomo Yitzhaki, 2006. "Inequality measurement and the time structure of household income in Israel," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 4(2), pages 153-179, August.
    5. Beare, Brendan K. & Seo, Juwon, 2014. "Time Irreversible Copula-Based Markov Models," Econometric Theory, Cambridge University Press, vol. 30(5), pages 923-960, October.
    6. Edna Schechtman & Shlomo Yitzhaki & Taina Pudalov, 2011. "Gini’s multiple regressions: two approaches and their interaction," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 67-99.
    7. Shibin Zhang, 2023. "A copula spectral test for pairwise time reversibility," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(5), pages 705-729, October.
    8. Sebastian Schweer & Christian H. Weiß, 2016. "Testing for Poisson arrivals in INAR(1) processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 503-524, September.
    9. Domenica Panzera & Paolo Postiglione, 2020. "Measuring the Spatial Dimension of Regional Inequality: An Approach Based on the Gini Correlation Measure," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 148(2), pages 379-394, April.
    10. Marcel Carcea & Robert Serfling, 2015. "A Gini Autocovariance Function for Time Series Modelling," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(6), pages 817-838, November.
    11. Klein, Ingo & Mangold, Benedikt, 2015. "Cumulative Paired 𝜙-Entropy," FAU Discussion Papers in Economics 07/2015, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    12. Charles Condevaux & Stéphane Mussard & Téa Ouraga & Guillaume Zambrano, 2020. "Generalized Gini linear and quadratic discriminant analyses," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 219-236, August.
    13. McCausland, William J., 2007. "Time reversibility of stationary regular finite-state Markov chains," Journal of Econometrics, Elsevier, vol. 136(1), pages 303-318, January.
    14. Joachim R. Frick & Jan Goebel & Edna Schechtman & Gert G. Wagner & Shlomo Yitzhaki, 2006. "Using Analysis of Gini (ANOGI) for Detecting Whether Two Subsamples Represent the Same Universe," Sociological Methods & Research, , vol. 34(4), pages 427-468, May.
    15. Zacharias Psaradakis & Marián Vávra, 2022. "Using Triples to Assess Symmetry Under Weak Dependence," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1538-1551, October.
    16. Gilles Zumbach, 2007. "Time reversal invariance in finance," Papers 0708.4022, arXiv.org.
    17. Emmanuel Jurczenko & Bertrand Maillet & Paul Merlin, 2008. "Efficient Frontier for Robust Higher-order Moment Portfolio Selection," Post-Print halshs-00336475, HAL.
    18. Francesco Giancaterini & Alain Hecq & Claudio Morana, 2022. "Is Climate Change Time-Reversible?," Econometrics, MDPI, vol. 10(4), pages 1-18, December.
    19. Joachim Frick & Jan Goebel, 2008. "Regional Income Stratification in Unified Germany Using a Gini Decomposition Approach," Regional Studies, Taylor & Francis Journals, vol. 42(4), pages 555-577.
    20. Carsten Schröder & Yolanda Golan & Shlomo Yitzhaki, 2014. "Inequality and the time structure of earnings: evidence from Germany," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 12(3), pages 393-409, September.

    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:spr:stpapr:v:60:y:2019:i:3:d:10.1007_s00362-016-0845-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.