A class of optimal tests for contemporaneous non‐causality in VAR models. (13th March 2013)

• Record Type: Journal Article
• Authors: Bramati, Maria Caterina
• Is Part Of: Journal of time series analysis. Volume 34:Number 3(2013:May)
• Page Start: 330
• Page End: 344
• Publication Date: 2013-03-13
• Subjects: Time-series analysis -- Periodicals; 519.232
• DOI: 10.1111/jtsa.12016
• Languages: English
• ISSNs: 0143-9782

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>The aim of this paper was to test for <italic>contemporaneous non‐causality</italic> defined by Granger (1969) between two groups of variables in a VAR(<italic>p</italic>) setting. Since contemporaneous correlation of the innovations is a necessary condition for contemporaneous causality (Pierce and Haugh, 1977), we focused on testing some restrictions on the covariance matrix of the noise. The class of the derived tests is locally asymptotically most stringent (in the Le Cam sense), invariant with respect to the group of block affine transformations and asymptotically invariant with respect to the group of continuous monotone radial transformations. Those tests are based on multivariate ranks of distances and multivariate signs of the o bservations and are shown to be asymptotically distribution free under very mild assumptions on the noise.</p> </abstract>