Predicting next bit in a non random sequence

I have a nonrandom sequence of bits - I'm able to tell that the sequence is nonrandom because I have performed on it the runs test, moreover the sequence presents autocorrelation at lag 1 equal to 0.4 (right before the cutoff) whereas the partial auto correlation function has a sinusoidal behaviour... any suggestion on how to exploit those regularities, without assuming that the sequence follows a binomial distribution?