Simulated maximum likelihood in nonlinear continuous-discrete state space models: importance sampling by approximate smoothing (Q1424631)

A state-space model is considered in which the unobserved state process \(y(t)\) is described by a system of stochastic differential equations (SDE). The measurements are \(z_i=h(y(t_i),t_i,\psi)+\varepsilon_i\), where \(h\) is a known function, \(\varepsilon_i\sim N(0,R(t_i,\psi))\), and \(\psi\) is an unknown parameter which is also involved in the SDE for \(y\). A Monte-Carlo procedure with importance sampling is developed for the likelihood computations. An AR(2) process, the Ginzburg-Landau model and models with stochastic volatility are considered as examples.