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Statistics and high-frequency data. (English) Zbl 1375.62025

Kessler, Mathieu (ed.) et al., Statistical methods for stochastic differential equations. Selected papers based on the presentations at the 7th séminaire Européen de statistiques on “Statistics for stochastic differential equations models”, La Manga del Mar Menor, Cartagena, Spain, May 7–12, 2007. Boca Raton, FL: CRC Press (ISBN 978-1-4398-4940-8/hbk; 978-1-4398-4976-7/ebook). Monographs on Statistics and Applied Probability 124, 191-310 (2012).
Summary: This short course is devoted to a few statistical problems related to the observation of a given process on a fixed time interval, when the observations occur at regularly spaced discrete times. This kind of observations may occur in many different contexts, but they are particularly relevant in finance: we do have now huge amounts of data on the prices of various assets, exchange rates, and so on, typically “tick data” which are recorded at every transaction time. So we are mainly concerned with the problems which arise in this context, and the concrete applications we will give are all pertaining to finance.
In some sense they are not “standard” statistical problems, for which we want to estimate some unknown parameter. We are rather concerned with the “estimation” of some random quantities. This means that we would like to have procedures that are as model-free as possible, and also that they are in some sense more akin to nonparametric statistics.
For the entire collection see [Zbl 1246.60005].

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60G51 Processes with independent increments; Lévy processes
62P05 Applications of statistics to actuarial sciences and financial mathematics
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