Singer, Hermann Continuous panel models with time dependent parameters. (English) Zbl 0921.62102 J. Math. Sociol. 23, No. 2, 77-98 (1998). Summary: Panel data are modeled as dynamic structural equations in continuous time \(t\) (stochastic differential equations). The continuously moving latent state vector \(y(t)\) is mapped to an observable discrete time series (or panel) \(z_{ni}=z_n(t_i)\) with the help of a measurement equation including errors of measurement (continuous discrete state space model). Therefore the approach is able to handle data with irregularly observed waves, missing values and arbitrarily interpolated exogenous influences (control variables). In order to model development and growth models, the system parameter matrices are assumed to be time dependent.It is shown how the likelihood function can be computed in this general linear setting by using a Kalman filter algorithm. The estimation method is tested in a simulation study using a bivariate growth model and applied to the Brownian bridge. Cited in 5 Documents MSC: 62M05 Markov processes: estimation; hidden Markov models 62P99 Applications of statistics 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) Keywords:panel data; continuous-discrete state space model; time dependent parameters; growth models; Kalman filter Software:LSDE PDFBibTeX XMLCite \textit{H. Singer}, J. Math. Sociol. 23, No. 2, 77--98 (1998; Zbl 0921.62102) Full Text: DOI References: [1] Abrikosov A. A., Methods of Quantum Field Theory in Statistical Physics (1963) · Zbl 0135.45003 [2] Anninger G., Sociological Methodology pp 187– (1986) [3] Arnold L., Stochastic Differential Equations (1974) · Zbl 0278.60039 [4] DOI: 10.2307/2330945 [5] Bergstrom A. R., Statistical Inference in Continuous Time Models (1976) · Zbl 0348.00027 [6] Bergstrom A. 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