Activity signature functions for high-frequency data analysis
AbstractWe define a new concept termed activity signature function, which is constructed from discrete observations of a continuous-time process, and derive its asymptotic properties as the sampling frequency increases. We show that the function is a useful device for estimating the activity level of the underlying process and in particular for deciding whether the process contains a continuous martingale. An application to $ /DM exchange rate over 1986-1999 indicates that a jump-diffusion model is more plausible than a pure-jump model. A second application to internet traffic at NASA servers shows that an infinite variation pure-jump model is appropriate for its modeling.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 154 (2010)
Issue (Month): 2 (February)
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Web page: http://www.elsevier.com/locate/jeconom
Activity index Blumenthal-Getoor index Jumps Levy process Realized power variation;
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