Sign Tests for Dependent Observations

The present paper introduces new sign tests for testing equality of conditional distributions of two (arbitrary) adapted processes as well as for testing conditionally symmetric martingale-difference assumptions. Our analysis is based on results that demonstrate randomization over ties in sign tests for equality of conditional distributions of two adapted sequences produces a stream of i.i.d. symmetric Bernoulli random variables. This reduces the problem of estimating the critical values of the tests to computing the quantiles or moments of Binomial or normal distributions. A similar proposition holds for randomization over zero values of three-valued random variables in a conditionally symmetric martyingale-difference sequence.