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Testing for Serial Independence: Beyond the Portmanteau Approach

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  • Luca Bagnato
  • Lucio De Capitani
  • Antonio Punzo

Abstract

Portmanteau tests are typically used to test serial independence even if, by construction, they are generally powerful only in presence of pairwise dependence between lagged variables. In this article, we present a simple statistic defining a new serial independence test, which is able to detect more general forms of dependence. In particular, differently from the Portmanteau tests, the resulting test is powerful also under a dependent process characterized by pairwise independence. A diagram, based on p-values from the proposed test, is introduced to investigate serial dependence. Finally, the effectiveness of the proposal is evaluated in a simulation study and with an application on financial data. Both show that the new test, used in synergy with the existing ones, helps in the identification of the true data-generating process. Supplementary materials for this article are available online.

Suggested Citation

  • Luca Bagnato & Lucio De Capitani & Antonio Punzo, 2018. "Testing for Serial Independence: Beyond the Portmanteau Approach," The American Statistician, Taylor & Francis Journals, vol. 72(3), pages 219-238, July.
    • Handle: RePEc:taf:amstat:v:72:y:2018:i:3:p:219-238
    DOI: 10.1080/00031305.2016.1264314
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    References listed on IDEAS

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    4. Bagnato, Luca & De Capitani, Lucio & Mazza, Angelo & Punzo, Antonio, 2015. "SDD: An R Package for Serial Dependence Diagrams," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 64(c02).
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    1. 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.

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