1The Local Level Model with a Markov Switching Drift

We propose a nonlinear state space model that includes an unobserved level component and an unobserved switching drift component. The level is estimated by simple exponential smoothing where at a certain time t, the level is expressed as a weighted sum of the observed data and the level at the previous period. The drift is represented by a variable that evolves according to a Markov chain of order one. A new Bayesian procedure, based on a mixture of forward and backward filtering iterations, is developed to compute the posterior distributions of the population parameters and the unobserved components. This model with two drifts is used to infer the US business cycle. Using the US growth national product we estimate the model where one drift coefficient represents the expected rate of growth during an expansion and the other drift coefficient represents the expected rate during a recession. The stability of the model is investigated over various time periods and compared against other Markov switching models