High-frequency sampling of a continuous-time ARMA process

摘要

Continuous-time autoregressive moving average (CARMA) processes have recently been used widely in the modelling of non-uniformly spaced data and as a tool for dealing with high-frequency data of the form YnΔ,n = 0, 1, 2,..., where A is small and positive. Such data occur in many fields of application, particularly in finance and in the study of turbulence. This article is concerned with the characteristics of the process (VnΔ)n∈Ζ when Δ is small and the underlying continuous-time process (Y,)t∈R is a specified CARMA process.