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Testing Serial Independence via Density-Based Measures of Divergence

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Abstract

This article reviews some nonparametric serial independence tests based on measures of divergence between densities. Among others, the well-known Kullback–Leibler, Hellinger, Tsallis, and Rosenblatt divergences are analyzed. Moreover, their copula-based version is taken into account. Via a wide simulation study, the performances of the considered serial independence tests are compared under different settings. Both single-lag and multiple-lag testing procedures are investigated to find out the best “omnibus” solution.

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Correspondence to Antonio Punzo.

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Bagnato, L., De Capitani, L. & Punzo, A. Testing Serial Independence via Density-Based Measures of Divergence. Methodol Comput Appl Probab 16, 627–641 (2014). https://doi.org/10.1007/s11009-013-9320-4

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Keywords

  • Serial independence
  • Divergence measures
  • Nonparametric density estimation
  • Copulas
  • Permutation tests
  • Multiple tests

AMS 2000 Subject Classifications

  • 37M10
  • 62G10
  • 62F03
  • 62M10
  • 62G07
  • 62F40