Both state-space models and Markov switching models have been highlyproductive paths for empirical research in macroeconomics and finance. This bookpresents recent advances in econometric methods that make feasible the estimation ofmodels that have both features. One approach, in the classical framework, approximates the likelihood function, the other, in the Bayesian framework, usesGibbs-sampling to simulate posterior distributions from data.The authors presentnumerous applications of these approaches in detail: decomposition of time seriesinto trend and cycle, a new index of coincident economic indicators, approaches tomodeling monetary policy uncertainty, Friedman's "plucking" model of recessions, thedetection of turning points in the business cycle and the question of whether boomsand recessions are duration-dependent, state-space models with heteroskedasticdisturbances, fads and crashes in financial markets, long-run real exchange rates, and mean reversion in asset returns.