Bayesian analysis of high-frequency water temperature time series through Markov switching autoregressive models

An hourly water temperature time series recorded at the Gairn catchment (Scotland) is analysed here along with seven covariates. Modelling river temperature time series is important due to its influence on stream biochemical processes and aquatic ecology. Due to its high complexity, the dynamics of the water temperature is investigated through non-homogeneous Markov switching autoregressive models (MSARMs) in order to efficiently tackle the non-linearity, non-Normality, non-stationarity, and long memory of the series, which are issues usually not considered by previous approaches to water temperature modelling. MSARMs are observed state-dependent autoregressive processes driven by an unobserved, or hidden, Markov chain. Bayesian inference, model choice, and stochastic variable selection are performed numerically by Markov chain Monte Carlo algorithms. Hence, it is possible to efficiently fit the data, reconstruct the sequence of hidden states, restore the missing values, classify the observations into a few regimes, and select the covariates that drive both the observed and the hidden process providing new insight on water temperature dynamics. Our proposal is very general and flexible and can be applied to any kind of environmental time series.