96These notes are devoted to a simple but important issue: how could we develop a model of a stochastic process that not only allows the individual observations, X(t), to be drawn from different distributions but where the transitions are not independent—or, more concretely, which not only allows X(t) to be drawn from a different distribution than X(t-1) but also allows the state at time t-1 to influence the probability of a transition. This kind of model will accommodate a situation where the process has persistent variance regimes, i.e., long runs of higher or lower variance than normal.