The sequential Cauchy combination test: Revisiting the inference of autocorrelated test statistics in finance
Nabil Bouamara  1, 2@  , Sébastien Laurent  3@  , Shuping Shi  4@  
1 : Katholieke Universiteit Leuven  (KUL)  -  Website
Faculty of Economics and Business, Naamsestraat 69, BE-3000, Leuven -  Belgium
2 : Vrije Universiteit Brussel  (VUB)  -  Website
Solvay Business School, Pleinlaan 2, 1050-Brussels -  Belgium
3 : Aix-Marseille University
Aix-Marseille Université - AMU
4 : Macquarie University  -  Website
Balaclava Road, North Ryde , NSW, 2109, Australia -  Australia

Liu and Xie (2020) propose the Cauchy combination test for an overall hypothesis. It combines n individual hypotheses for which the test statistics are characterized by sparsity and arbitrary dependency structures. It is not obvious how statements about individual hypotheses are to be made for this procedure. We unravel the combination test to make statements on the elementary hypotheses. It is based on the principle of closed testing and controls the multiple level alpha. We show the benefits of our approach by revisiting the attenuation bias in the autocorrelated drift-burst z statistics of Christensen, Oomen, and Renò (2020).


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