Model fitting for continuous-time stationary processes from discrete-time data

AbstractLet X = {X(t), −∞<t<∞} be a continuous-time stationary process with spectral density φX(λ; θ), where θ is a vector of unknown parameters. Let {τk} be a stationary point process on the real line which is independent of X. The identifiability and the estimation of θ from the discrete-time observation {X(τk), τk} are considered. The consistency of appropriate estimates θT as the time Tå∞ is extablished and a central limit theorem for θT is given