Introducing non-linear dynamics to the two-regime market model: Evidence

The existing two-regime asset-pricing models do not reach a consensus, either in the definition of bull and bear market conditions or in the modelling of beta non-stationarity. We apply a logistic smooth transition regression model to address the beta non-stationarity issue. Using eight different definitions of bull and bear market conditions, we intend to ascertain the most appropriate definition with which to capture the non-linear dynamics of security returns. We find, through a series of linearity tests, that the Logistic Smooth Transition Market (LSTM) model provides an adequate description of the data generating process. Further, we explore the adequacy of a duration dependent description of market conditions in our model. Often we find that the 4-month lagged yield spread is a more appropriate definition of market condition than is a coincident economic indicator, excess market returns and a moving average of excess market returns. We also find duration dependence in market conditions.