High-frequency sampling of a continuous-time ARMA processes

Interest in continuous-time processes has increased rapidly in recent years, largely because of the high-frequency data available in many areas of application, particularly in finance and turbulence. We develop a method for estimating the kernel function of a continuous-time moving average (CMA) process Y which takes advantage of the high-frequency of the data. In order to do so we examine the relation between the CMA process Y and the discrete-time process $Y^\Delta$ obtained by sampling Y at times which are integer multiples of some small positive $\Delta$. In particular we derive asymptotic results as $\Delta\downarrow 0$ which generalize results of Brockwell, Ferrazzano and Klüppelberg (2011) for high-frequency sampling of CARMA processes. We propose an estimator of the continuous-time kernel based on observations of $Y^\Delta$, investigate its properties and illustrate its performance using simulated data. Particular attention is paid to the performance of the estimator as $\Delta\downarrow 0$. Time-domain and frequency-domain methods are used to obtain insight into CMA processes and their sampled versions.     «

Interest in continuous-time processes has increased rapidly in recent years, largely because of the high-frequency data available in many areas of application, particularly in finance and turbulence. We develop a method for estimating the kernel function of a continuous-time moving average (CMA) process Y which takes advantage of the high-frequency of the data. In order to do so we examine the relation between the CMA process Y and the discrete-time process $Y^\Delta$ obtained by samplin...     »