A new nonlinearity test to circumvent the limitation of Volterra expansion with application

Yongchang HUI, Wing Keung WONG, Zhidong BAI, Zhen Zhen ZHU

Research output: Journal PublicationsJournal Article (refereed)peer-review

14 Citations (Scopus)


In this paper, we propose a quick and efficient method to examine whether a time series Xt possesses any nonlinear feature by testing a kind of dependence remained in the residuals after fitting Xt with a linear model. The advantage of our proposed nonlinearity test is that it is not required to know the exact nonlinear features and the detailed nonlinear forms of the variable being examined. Another advantage of our proposed test is that there is no over-rejection problem which exists in some famous nonlinearity tests. Our proposed test can also be used to test whether the hypothesized model, including linear and nonlinear, to the variable being examined is appropriate as long as the residuals of the model being used can be estimated. Our simulation study shows that our proposed test is stable and powerful. We apply our proposed statistic to test whether there is any nonlinear feature in the sunspot data. The conclusion drawn from our proposed test is consistent with those from other well-established tests.
Original languageEnglish
Pages (from-to)365-374
Number of pages10
JournalJournal of the Korean Statistical Society
Issue number3
Publication statusPublished - 1 Sep 2017
Externally publishedYes


  • Dependence
  • Dependent test
  • Nonlinear test
  • Nonlinearity
  • Sunspots
  • Volterra expansion


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