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Davy Paindaveine, ECARES Print
Friday, 05 March 2010, 12:15 - 13:15

On Multivariate Runs Tests for Randomness

Davy Paindaveine, ECARES, ULB

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. 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. A Monte-Carlo study investigates the small-sample properties of the proposed procedures. A real data example is treated and shows that combining various runs tests runs may provide some insight on the reason why rejection occurs.

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