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Continuous-time state-space models (SSMs) are flexible tools for analysingirregularly sampled sequential observations that are driven by an underlyingstate process. Corresponding applications typically involve restrictiveassumptions concerning linearity and Gaussianity to facilitate inference on themodel parameters via the Kalman filter. In this contribution, we provide ageneral continuous-time SSM framework, allowing both the observation and thestate process to be non-linear and non-Gaussian. Statistical inference iscarried out by maximum approximate likelihood estimation, where multiplenumerical integration within the likelihood evaluation is performed via a finediscretisation of the state process. The corresponding reframing of the SSM asa continuous-time hidden Markov model, with structured state transitions,enables us to apply the associated efficient algorithms for parameterestimation and state decoding. We illustrate the modelling approach in a casestudy using data from a longitudinal study on delinquent behaviour ofadolescents in Germany, revealing temporal persistence in the deviation of anindividual's delinquency level from the population mean.

Maximum approximate likelihood estimation of general continuous-time state-space models