How are sequences used to predict future events?

Hmm. Usually when I think of predicting future events, I think in terms of Markov Chains. Perhaps the most interesting aspect of Markov chains is the study of a chain's long-term behavior. For instance, we can use it for voting after many elections have passed (assuming that the given stochastic matrix continues to describe the transition percentages from one election to the next). In which case, we can use a steady-state vector to determine the probability of an event happening in the future.

Just some of my thoughts on that.