Regime Switching Models
The states of the market are conventionally called Bull and Bear. The states of the economy are referred to as recession, recovery, expansion, contraction. The popular financial press repeats the conventional wisdom relating to the definition of Bull and Bear markets. The simplest definition of Bull and Bear states would be to label a month as a Bear month if the market index went down in that month and as a Bull month if the market index went up in that month. A model with separate Bull and Bear distributions can be considered. There can be a mean and variance for the Bull state and another mean and variance for the Bear state. Bull markets have a declining hazard function although the best market gains come at the start of a Bull market.