Paper detail

High frequency sampling of a continuous-time ARMA process

Continuous-time autoregressive moving average (CARMA) processes have recently been used widely in the modeling of non-uniformly spaced data and as a tool for dealing with high-frequency data of the form $Y_{nΔ}, n=0,1,2,...$, where $Δ$ is small and positive. Such data occur in many fields of application, particularly in finance and the study of turbulence. This paper is concerned with the characteristics of the process $(Y_{nΔ})_{n\in\bbz}$, when $Δ$ is small and the underlying continuous-time process $(Y_t)_{t\in\bbr}$ is a specified CARMA process.