Recursive residuals and model diagnostics for normal and non-normal state space models

Model diagnostics for normal and non-normal state space models are based on recursive residuals which are defined from the one-step ahead predictive distribution. Routine calculation of these residuals is discussed in detail. Various diagnostic tools are suggested to check, for example, for wrong observation distributions and for autocorrelation. The paper also discusses such topics as model diagnostics for discrete time series and model discrimination via Bayes factors. The case studies cover environmental applications such as analysing a time series of the number of daily rainfall occurrences and a time series of daily sulfur dioxide emissions.