The econometrics of high-frequency data.

*(English)*Zbl 1375.62023
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, 109-190 (2012).

From the introduction: This is a course on estimation in high frequency data. It is intended for an audience that includes
interested people in finance, econometrics, statistics, probability and financial engineering. \(\dots\)

The purpose of this article, however, is not so much to focus on the applications as on the probabilistic setting and the estimation methods. The theory was started, on the probabilistic side, by Jacod (1994) and Jacod and Protter (1998), and on the econometric side by Foster and Nelson (1996) and Comte and Renault (1998). The econometrics of integrated volatility was pioneered in Andersen, Bollerslev, Diebold, and Labys (2001, 2003), Barndorff-Nielsen and Shephard (2002, 2004b) and Dacorogna, Gençay, Müller, Olsen, and Pictet (2001). The authors of this article started to work in the area through Zhang (2001), Zhang, Mykland, and Aït-Sahalia (2005), and Mykland and Zhang (2006).

This article is meant to be a moderately self-contained course into the basics of this material. The introduction assumes some degree of statistics/econometric literacy, but at a lower level than the standard probability text. Some of the material is research front and not published elsewhere. This is not meant as a full review of the area.

The text also mostly overlooks the questions that arise in connection with multidimensional processes.

For the entire collection see [Zbl 1246.60005].

The purpose of this article, however, is not so much to focus on the applications as on the probabilistic setting and the estimation methods. The theory was started, on the probabilistic side, by Jacod (1994) and Jacod and Protter (1998), and on the econometric side by Foster and Nelson (1996) and Comte and Renault (1998). The econometrics of integrated volatility was pioneered in Andersen, Bollerslev, Diebold, and Labys (2001, 2003), Barndorff-Nielsen and Shephard (2002, 2004b) and Dacorogna, Gençay, Müller, Olsen, and Pictet (2001). The authors of this article started to work in the area through Zhang (2001), Zhang, Mykland, and Aït-Sahalia (2005), and Mykland and Zhang (2006).

This article is meant to be a moderately self-contained course into the basics of this material. The introduction assumes some degree of statistics/econometric literacy, but at a lower level than the standard probability text. Some of the material is research front and not published elsewhere. This is not meant as a full review of the area.

The text also mostly overlooks the questions that arise in connection with multidimensional processes.

For the entire collection see [Zbl 1246.60005].

##### MSC:

62M09 | Non-Markovian processes: estimation |

62P05 | Applications of statistics to actuarial sciences and financial mathematics |

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |

62P20 | Applications of statistics to economics |

91B82 | Statistical methods; economic indices and measures |

91G70 | Statistical methods; risk measures |