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Non parametric portmanteau tests for detecting non linearities in high dimensions

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  • Jan G. De Gooijer
  • Ao Yuan

Abstract

We propose two non parametric portmanteau test statistics for serial dependence in high dimensions using the correlation integral. One test depends on a cutoff threshold value, while the other test is freed of this dependence. Although these tests may each be viewed as variants of the classical Brock, Dechert, and Scheinkman (BDS) test statistic, they avoid some of the major weaknesses of this test. We establish consistency and asymptotic normality of both portmanteau tests. Using Monte Carlo simulations, we investigate the small sample properties of the tests for a variety of data generating processes with normally and uniformly distributed innovations. We show that asymptotic theory provides accurate inference in finite samples and for relatively high dimensions. This is followed by a power comparison with the BDS test, and with several rank-based extensions of the BDS tests that have recently been proposed in the literature. Two real data examples are provided to illustrate the use of the test procedure.

Suggested Citation

  • Jan G. De Gooijer & Ao Yuan, 2016. "Non parametric portmanteau tests for detecting non linearities in high dimensions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(2), pages 385-399, January.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:2:p:385-399
    DOI: 10.1080/03610926.2013.815209
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    Cited by:

    1. De Gooijer, Jan G., 2023. "On portmanteau-type tests for nonlinear multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 195(C).

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