This dissertation has for prime theme the exploration of nonlinear econometric models featuring a hidden Markov chain. Occasional and discrete shifts in regimes generate convenient nonlinear dynamics to econometric models, allowing for structural changes similar to the exogenous economic events occurring in reality. The first paper sets up a Monte Carlo experiment to explore the finite-sample properties of the estimates of vector autoregressive models subject to switches in regime governed by a hidden Markov chain. The main finding of this article is that the accuracy with which regimes are determined by the Expectation Maximixation algorithm shows improvement when the dimension of the simulated series increases. However this gain comes at the cost of higher sample size requirements for models with more variables. The second paper advocates the use of Bayesian impulse responses for a Markovswitching Vector Autoregressive model. These responses are sensitive to the Markovswitching properties of the model and, based on densities, allow statistical inference to be conducted. Upon the premise of structural changes occurring on oil markets, the empirical results of Kilan (2009) are reinvestigated. The effects of the structural shocks are characterized over four estimated regimes. Over time, the regime dynamics are evolving into more competitive oil markets, with the collapse of the OPEC. Finally, the third paper proposes a method of testing restrictions for Granger noncausality in mean, variance and distribution in the framework of Markov-switching VAR models. Due to the nonlinearity of the restrictions derived by Warne (2000), classical tests have limited use. Bayesian inference consists of a novel Block Metropolis-Hastings sampling algorithm for the estimation of the restricted models, and of standard methods of computing posterior odds ratios. The analysis may be applied to financial and macroeconomic time series with changes of parameter values over time and heteroskedasticity.