High frequency sampling of a continuous-time ARMA process

TL;DR

This paper investigates the properties of high-frequency sampled data from continuous-time CARMA processes, focusing on the behavior as the sampling interval becomes very small, relevant for finance and turbulence modeling.

Contribution

It characterizes the sampling behavior of CARMA processes at high frequency, providing insights into their properties when discretely observed at small intervals.

Findings

Analysis of the asymptotic behavior of sampled CARMA processes

Characterization of the process's properties as sampling interval approaches zero

Implications for modeling high-frequency financial and turbulence data

Abstract

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 $Y_{n\Delta}, n=0,1,2,...$, where $\Delta$ 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 $(Y_{n\Delta})_{n\in\bbz}$, when $\Delta$ is small and the underlying continuous-time process $(Y_t)_{t\in\bbr}$ is a specified CARMA process.