Exact significance test for Markov order

We describe an exact significance test of the null hypothesis that a Markov chain is n th order. The procedure utilizes surrogate data to yield an exact test statistic distribution valid for any sample size. Surrogate data are generated using a novel algorithm that guarantees, per shot, a uniform sampling from the set of sequences that exactly match the n th order properties of the observed data. Using the test, the Markov order of Tel Aviv rainfall data is examined.