This paper 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 adapt the Monte Carlo test method to non-continuous 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 non-spurious power gains (over standard combination methods) can be achieved through the combined Monte Carlo test approach, and confirm arguments in favour of variance-ratio type criteria.

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