Periodic multivariate Normal hidden Markov models for the analysis of water quality time series

The modelling of multivariate riverine water quality time series poses some challenging problems including: weak dependency between observations; nonlinearity; non-Normality; seasonality and missing data. We demonstrate that periodic multivariate Normal hidden Markov models (MNHMMs) are appropriate tools to analyse riverine water quality time series. We introduce a fully Bayesian inference procedure for this class of models, where the number of hidden states of the Markov process is unknown and reversible jump Markov chain Monte Carlo (RJMCMC) methods are developed. We present a case study using long-term dissolved inorganic nitrogen time series measured in three Scottish rivers. Our results show the strength of the hidden Markov multistate approach for analysing long-term multivariate riverine water quality time series.