A model sufficiency test using permutation entropy

Xin Huang, Han Lin Shang*, David Pitt

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Using the ordinal-pattern concept in permutation entropy, we propose a model sufficiency test to study a given model's point prediction accuracy. Compared with some classical model sufficiency tests, such as Broock et al.'s (1996) test, our proposal does not require a sufficient model to eliminate all structures exhibited in the estimated residuals. When the innovations in the investigated data's underlying dynamics show a certain structure, such as higher moment serial dependence, Broock et al.'s (1996) test can lead to erroneous conclusions about the sufficiency of point predictors. Due to the structured innovations, inconsistency between the model sufficiency tests and prediction accuracy criteria can occur. Our proposal fills in this incoherence between model and prediction evaluation approaches and remains valid when the underlying process has nonwhite additive innovation.

Original languageEnglish
Pages (from-to)1017-1036
Number of pages20
JournalJournal of Forecasting
Issue number5
Early online date3 Jan 2022
Publication statusPublished - Aug 2022


  • Bivariate dependence
  • BDS test
  • Model evaluation
  • Ordinal pattern
  • Prediction accuracy


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