Asymptotic properties of functionals of increments of a continuous semimartingale with stochastic sampling times
نویسندگان
چکیده
This paper is concerned with asymptotic behavior of a variety of functionals of increments of continuous semimartingales. Sampling times are assumed to follow a rather general discretization scheme. If an underlying semimartingale is thought of as a financial asset price process, a general sampling scheme like the one employed in this paper is capable of reflecting what happens whenever the financial trading data are recorded in a tick-by-tick fashion. A law of large numbers and a major central limit theorem are proved after an appropriate normalization. Applications of our results include statistical estimation and inference for high-frequency financial data models.
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