Abstract
This study introduces a Hidden Markov quantile model with trend dynamics. This methodology allows one to focus on regime switches observed not only on the median but also on some other upper and lower time‐trend extremes observed in air temperature data. In practice, we propose some semi‐parametric quantile trend models with hidden states which can be modelled using the Asymmetric Laplace distribution. Our estimation is based on a Bayesian early‐rejection Markov chain Monte Carlo algorithm. By using simulated data, we investigate the sampling properties of the proposed methodology. The real data results, taken from some global surface temperatures generated by NASA and from some mean monthly homogenised air temperature series in Greece, mostly show that the two‐state Hidden Markov quantile time‐trend model is the most predominant one compared to other state models showing heterogeneities affected by the analysed periods, data types and quantile levels.