How can neuronal networks with local learning rules predict their future inputs?
see Lisman, J. E. and Otmakhova, N. A. (2001), Storage, recall, and novelty detection of sequences by the hippocampus: Elaborating on the SOCRATIC model to account for normal and aberrant effects of dopamine. Hippocampus, 11: 551–568. doi: 10.1002/hipo.1071: http://wwww.bio.brandeis.edu/lismanlab/pdf/socratic.pdf for one proposed mechanism.

in short, local learning rules can develop connections between items that occur sequentially.  if you have one network that pattern completes (i.e. identifies) the input, you can pass that identification to a second network which learns temporal associations between items.