On multivariate runs tests for randomness

Davy Paindaveine

No 2009_002, Working Papers ECARES from ULB -- Universite Libre de Bruxelles

Abstract: This paper proposes several extensions of the concept of runs to the multivariate setup, and studies the resulting tests of multivariate randomness against serial dependence. Two types of multivariate runs are defined: (i) an elliptical extension of the spherical runs proposed by Marden (1999), and (ii) an original concept of matrix-valued runs. The resulting runs tests themselves exist in various versions, one of which is a function of the number of data-based hyperplanes separating pairs of observations only. All proposed multivariate runs tests are affine-invariant and highly robust: in particular, they allow for heteroskedasticity and do not require any moment assumption. Their limiting distributions are derived under the null hypothesis and under sequences of local vector ARMA alternatives. Asymptotic relative efficiencies with respect to Gaussian Portmanteau tests are computed, and show that, while Mardentype runs tests suffer severe consistency problems, tests based on matrix-valued runs perform uniformly well for moderate-to-large dimensions. A Monte-Carlo study confirms the theoretical results and investigates the robustness properties of the proposed procedures. A real data example is also treated, and shows that combining both types of runs tests may provide some insight on the reason why rejection occurs, hence that Marden-type runs tests, despite their lack of consistency, also are of interest for practical purposes.

Keywords: elliptical distributions; interdirections (search for similar items in EconPapers)
Date: 2009
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (9)

Published by: ECARES

Downloads: (external link)
https://dipot.ulb.ac.be/dspace/bitstream/2013/5754 ... _wpaper_2009_002.pdf RePEc_eca_wpaper_2009_002 (application/pdf)

Related works:
Journal Article: On Multivariate Runs Tests for Randomness (2009)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eca:wpaper:2009_002

Ordering information: This working paper can be ordered from
http://hdl.handle.ne ... ulb.ac.be:2013/57547

Access Statistics for this paper

More papers in Working Papers ECARES from ULB -- Universite Libre de Bruxelles Contact information at EDIRC.
Bibliographic data for series maintained by Benoit Pauwels ().