SEM modeling with singular moment matricesPart II: ML-Estimation of sampled stochasticdierential equations

Linear stochastic dierential equations (SDE) are expressed as an exactdiscrete model (EDM) and estimated with structural equation models(SEM) and the Kalman lter (KF) algorithm. The SEM likelihood is welldened even for the times series case and the SEM and KF approach yieldthe same likelihood. The oversampling approach is introduced in orderto formulate the EDM on a time grid which is ner than the samplingintervals. This leads to a simple computation of the nonlinear parameterfunctionals of the EDM. For small discretization intervals, the functionalscan be linearized and software permitting only linear parameter restrictionscan be used. However, in this case the SEM approach must handlelarge matrices leading to degraded performance and possible numericalproblems. The methods are compared using coupled linear random oscillatorswith time varying parameters and irregular sampling times....