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Optimal rank-based tests for block exogeneity in vector autoregressions

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  • Bramati, Maria Caterina

Abstract

The aim of this paper is to construct a class of locally asymptotically most stringent (in the Le Cam sense) tests for independence between two sets of variables in the V AR models. These tests are based on multivariate ranks of distances and multivariate signs of the observations and are shown to be asymptotically distribution-free under very mild assumptions on the noise, which is obtained by applying a linear transformation to marginally spherical innovations. The class of tests derived is invariant with respect to the group of block affine transformations and asymptotically invariant with respect to the group of continuous monotone marginal radial transformations.

Suggested Citation

  • Bramati, Maria Caterina, 2013. "Optimal rank-based tests for block exogeneity in vector autoregressions," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 141-162.
    • Handle: RePEc:eee:jmvana:v:116:y:2013:i:c:p:141-162
    DOI: 10.1016/j.jmva.2012.12.003
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    References listed on IDEAS

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    1. Marc Hallin & Madan Lal Puri, 1994. "Aligned rank tests for linear models with autocorrelated errors," ULB Institutional Repository 2013/2045, ULB -- Universite Libre de Bruxelles.
    2. Swensen, Anders Rygh, 1985. "The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend," Journal of Multivariate Analysis, Elsevier, vol. 16(1), pages 54-70, February.
    3. Hallin, Marc & Saidi, Abdessamad, 2007. "Optimal Tests of Noncorrelation Between Multivariate Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 938-951, September.
    4. Bernard Garel & Marc Hallin, 1995. "Local asymptotic normality of multivariate ARMA processes with a linear trend," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 551-579, September.
    5. Hallin, Marc & Paindaveine, Davy, 2005. "Affine-invariant aligned rank tests for the multivariate general linear model with VARMA errors," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 122-163, March.
    6. Hallin, M. & Puri, M. L., 1994. "Aligned Rank Tests for Linear Models with Autocorrelated Error Terms," Journal of Multivariate Analysis, Elsevier, vol. 50(2), pages 175-237, August.
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