A Variational Approach to Continuous Time Dynamic Models

In this chapter we introduce a new approach to parameter estimation in continuous time modeling in the spirit of variational data assimilation or machine learning. This is a purely time-continuous approach relying on the theory of optimization for dynamical systems. We complement the proposed algorithm with a practical example, comparing the results of this approach to those obtained via Continuous Time Structural Equation Modeling (ctsem). To this end, we assess the reciprocal relationship between satisfaction with health and satisfaction with work using data from the German Socio-Economic Panel. It turns out that the proposed algorithm determines a drift matrix whose principle directions (eigenvectors) are qualitatively equivalent to the ones estimated via ctsem, but the associated eigenvalues differ substantially, leading to quantitatively different conclusions.