Statistical Modelling 24 (1) (2024), 9–28

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

Sina Mews,
Department of Business Administration and Economics,
Bielefeld University,
Bielefeld,
Germany.
e-mail: sina.mews@uni-bielefeld.de

Roland Langrock,
Department of Business Administration and Economics,
Bielefeld University,
Bielefeld,
Germany.

Marius Ötting,
Department of Business Administration and Economics,
Bielefeld University,
Bielefeld,
Germany.

Houda Yaqine,
Department of Business Administration and Economics,
Bielefeld University,
Bielefeld,
Germany.

Jost Reinecke,
Faculty of Sociology,
Bielefeld University,
Bielefeld,
Germany.

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 discretization 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.

Keywords:

hidden Markov model (HMM), Irregular time intervals, non-Gaussian and non-linear processes, Ornstein-Uhlenbeck process, sequential data.

Downloads:

Data and code in tar.gz archive, Supplementary material in PDF.

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