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This study deals with the problem of fitting a time series modeled by a smooth transition regression function. This model extends the standard linear piecewise model. Within the piecewise model, the regression function parameters change abruptly at the changepoints. In the smooth transition model, parametric transition functions are introduced that allow for gradual changes of the regression function around the changepoints. This model can very accurately reproduce both nonregular and smooth random processes. Moreover it allows the extraction of information about the changes in the regression function through the transition function parameters. The estimation of the model is performed through a fully Bayesian framework. Prior distributions are set for each parameter and the full joint posterior distribution is expressed. The computation of standard Bayesian estimates involves intractable multi-dimensional integrals. Therefore, a reversible-jump Markov chain Monte-Carlo algorithm is derived to sample the joint posterior distributions. A comparative simulation study shows that the smooth transition approach achieves competitive performances and provides more sparse representations of standard test functions. Finally, the smooth transition framework is applied to estimate real world electrical transients, which allows the extraction of the relevant features for signal classification.