Model fitting for continuous-time stationary processes from discrete-time data (Q1186773)

Let \(\{x(t),-\infty<t<\infty\}=X\) be a continuous-time stationary process, with spectral density \(f(\lambda;\underset\widetilde{}{\theta})\), where \(\underset\widetilde{}{\theta}\) is a vector of unknown parameters. Let \(\{\tau_ k\}\) be a stationary point process on the real line, independent of \(X\). Based on discrete-time observations \(\{X(\tau_ k),\tau_ k\}\), consistent estimates \(\underset\widetilde{}{\hat\theta}_ T\) are considered and a central limit theorem for them is given.