**Acknowledgements**

The authors thank the Editor for sending comments that helped to improve the presentation of the results. The authors also thank Peter Guttorp for providing a copy of his works related to applications of non-homogeneous Markov chains. ERR and MHT were partially funded by the project PAPIIT-IN102713-3 of the Dirección General de Apoyo al Personal Académico de la Universidad Nacional Autónoma de México (DGAPA-UNAM), Mexico. ERR also received funds from a sabbatical year grant from DGAPA-UNAM. ERR is grateful to the Departments of Statistics of the Universidade Estadual Paulista "Júlio de Mesquita Filho" – Campus Presidente Prudente, Brazil, and of the University of Oxford, UK, where parts of this work were developed, for all the support and hospitality received during her stay at those departments.
