You can come up with a mean-reverting stochastic model which might superficially replicate the periods of "stable" prices. This could be extended to a model in which there are two nearby "stable" prices, in which case the stochastic model would look superficially similar to what rdf posted. You could then imagine that the position of the "stable" prices and their relative stabllity would change slowly with time. This would entail that after jumping back and forth the "square wave" would not return exactly to the previous "stable" level. Finally, you could model a the emergence of a new regime. Initially you would have just a single stable price but then a second stable point would develop and gradually become dominant. For the period where neither of the two points is dominant you would observe jumps back and forth in rdf's square wave fashion. Eventually the new regime would take over.

Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith