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High-frequency sampling of a continuous-time ARMA process


Vincenzo Ferrazzano, Center for Mathematical Sciences, Technische Universität München, 85748 Garching b. München, Germany.



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 inline image,n = 0, 1, 2,…, where Δ 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 inline image, when Δ is small and the underlying continuous-time process inline image is a specified CARMA process.