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A diagram to detect serial dependencies: an application to transport time series

Author

Listed:
  • Luca Bagnato

    (Università Cattolica del Sacro Cuore)

  • Lucio De Capitani

    (Università di Milano-Bicocca)

  • Antonio Punzo

    (Università di Catania)

Abstract

The Ljung–Box test is typically used to test serial independence even if, by construction, it is generally powerful only in presence of pairwise linear dependence between lagged variables. To overcome this problem, Bagnato et al. recently proposed a simple statistic defining a serial independence test which, differently from the Ljung–Box test, is powerful also under a linear/nonlinear dependent process characterized by pairwise independence. The authors also introduced a normalized bar diagram, based on p-values from the proposed test, to investigate serial dependence. This paper proposes a balanced normalization of such a diagram taking advantage of the concept of reproducibility probability. This permits to study the strength and the stability of the evidence about the presence of the dependence under investigation. An illustrative example based on an artificial time series, as well as an application to a transport time series, are considered to appreciate the usefulness of the proposal.

Suggested Citation

  • Luca Bagnato & Lucio De Capitani & Antonio Punzo, 2017. "A diagram to detect serial dependencies: an application to transport time series," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(2), pages 581-594, March.
    • Handle: RePEc:spr:qualqt:v:51:y:2017:i:2:d:10.1007_s11135-016-0426-y
    DOI: 10.1007/s11135-016-0426-y
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    References listed on IDEAS

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    1. Heather M. Anderson & Farshid Vahid, 2005. "Nonlinear Correlograms and Partial Autocorrelograms," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(s1), pages 957-982, December.
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    4. Marc Hallin & Guy Melard, 1988. "Rank-based tests for randomness against first-order serial dependence," ULB Institutional Repository 2013/2015, ULB -- Universite Libre de Bruxelles.
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    6. De Capitani, L. & De Martini, D., 2011. "On stochastic orderings of the Wilcoxon Rank Sum test statistic--With applications to reproducibility probability estimation testing," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 937-946, August.
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    10. L. Bagnato & L. De Capitani & A. Punzo, 2016. "The Kullback–Leibler autodependogram," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(14), pages 2574-2594, October.
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    1. Lucio De Capitani & Daniele De Martini, 2021. "Improving reproducibility probability estimation and preserving RP-testing," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 49-77, March.

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