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

TL;DR

This paper introduces a flexible continuous-time state-space model framework that handles non-linear and non-Gaussian processes, enabling more accurate inference from irregularly sampled data through maximum approximate likelihood estimation.

Contribution

It extends traditional linear Gaussian models by allowing non-linearity and non-Gaussianity, and develops efficient algorithms for parameter estimation and state decoding.

Findings

Applied to adolescent delinquency data, revealing persistence in delinquency deviations.

Demonstrated the model's ability to handle complex, real-world longitudinal data.

Showed improved inference accuracy over traditional models.

Abstract

Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions concerning linearity and Gaussianity to facilitate inference on the model parameters via the Kalman filter. In this contribution, we provide a general continuous-time SSM framework, allowing both the observation and the state process to be non-linear and non-Gaussian. Statistical inference is carried out by maximum approximate likelihood estimation, where multiple numerical integration within the likelihood evaluation is performed via a fine discretisation of the state process. The corresponding reframing of the SSM as a continuous-time hidden Markov model, with structured state transitions, enables us to apply the associated efficient algorithms for parameter estimation and state decoding. We illustrate the modelling approach in a case study using data from a longitudinal study on delinquent behaviour of adolescents in Germany, revealing temporal persistence in the deviation of an individual's delinquency level from the population mean.