Fermín, LisandroLisandroFermínJosé MarcanoLuis-Angel Rodríguez2025-12-072025-12-072021-12-2910.1016/j.spl.2021.1093472-s2.0-85122651001https://cris-uv-2.scimago.es/handle/123456789/7299WOS:000789652600010We propose a new approach to demonstrate the consistency of the maximum likelihood estimator for nonlinear Markov-switching AR processes (abbreviated MS-NAR). We obtain a uniform exponential memory loss property for the prediction filter by approximating it by a filter with finite memory. From the α-mixing property for the MS-NAR process we obtain an ergodic theorem. Finally, we show that in the linear and Gaussian case our assumptions are fully satisfied.enacceso restringidoStatistics And ProbabilityStatistics, Probability And Uncertaintyarticle