Environmental time series analysis and forecasting with the Captain toolbox

The Data-Based Mechanistic (DBM) modelling philosophy emphasises the importance of parametrically efficient, low order, ‘dominant mode’ models, as well as the development of stochastic methods and the associated statistical analysis required for their identification and estimation. Furthermore, it stresses the importance of explicitly acknowledging the basic uncertainty in the process, which is particularly important for the characterisation and forecasting of environmental and other poorly defined systems. The paper focuses on a Matlab® compatible toolbox that has evolved from this DBM modelling research. Based around a state space and transfer function estimation framework, Captain extends Matlab® to allow, in the most general case, for the identification and estimation of a wide range of unobserved components models. Uniquely, however, Captain focuses on models with both time variable and state dependent parameters and has recently been implemented with the latest methodological developments in this regard. Here, the main innovations are: the automatic optimisation of the hyper-parameters, which define the statistical properties of the time variable parameters; the provision of smoothed as well as filtered parameter estimates; the robust and statistically efficient identification and estimation of both discrete and continuous time transfer function models; and the availability of various special model structures that have wide application potential in the environmental sciences.