As we consider here a binary alphabet (k = 2) and a first order Markov model (m = 1) we have only km(k - 1) = 2 parameters to estimate with a sample of size n = 5000 (so we have 2500 sample per parameter). Although this situation seems quite comfortable, the sensitivity to parameter estimation appears in fact to be so large that we could have a factor 1040 between the true p-value and its estimate.