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

Abstract

Let X = { X( t), −∞< t<∞} be a continuous-time stationary process with spectral density φ X (λ; θ), where θ is a vector of unknown parameters. Let { τ k } 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( τ k ), τ k } are considered. The consistency of appropriate estimates θ T as the time T a ̊ ∞ is extablished and a central limit theorem for θ T is given.