This article suggests Monte Carlo multiple test procedures which are provably valid in finite samples. These include combination methods originally proposed for independent statistics and further improvements which formalize statistical practice. We also adopt the Monte Carlo test method to noncontinuous combined statistics. The methods suggested are applied to test serial dependence and predictability. In particular, we introduce and analyze new procedures that account for endogenous lag selection. A simulation study illustrates the properties of the proposed methods. Results show that concrete and nonspurious power gains (over standard combination methods) can be achieved through the combined Monte Carlo test approach, and confirm arguments in favor of variance-ratio type criteria.

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Keywords Induced test, Monte Carlo test, Simultaneous inference, Test combination, Variance ratio
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Journal Communications in Statistics Part B: Simulation and Computation
Dufour, J.-M. (Jean-Marie), Khalaf, L, & Voia, M.-C. (2015). Finite-sample Resampling-based Combined Hypothesis Tests, with Applications to Serial Correlation and Predictability. In Communications in Statistics Part B: Simulation and Computation (Vol. 44, pp. 2329–2347). doi:10.1080/03610918.2013.858164