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High-Frequency Financial Econometrics$
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Yacine Aït-Sahalia and Jean Jacod

Print publication date: 2014

Print ISBN-13: 9780691161433

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691161433.001.0001

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With Jumps: An Introduction to Power Variations

With Jumps: An Introduction to Power Variations

Chapter:
(p.109) Chapter 4 With Jumps: An Introduction to Power Variations
Source:
High-Frequency Financial Econometrics
Author(s):

Yacine Aïıt-Sahalia

Jean Jacod

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691161433.003.0004

This chapter studies the simplest possible process having both a non-trivial continuous part and jumps. It starts with the asymptotic behavior of power variations when the model is nonparametric, that is, without specifying the law of the jumps. This is done in the same spirit as in Chapter 3: the ideas for the proofs are explained in detail, but technicalities are omitted. Then, it considers the use of these variations in a parametric estimation setting based on the generalized method of moments. There, it considers the ability of certain moment functions, corresponding to power variations, to achieve identification of the parameters of the model and the resulting rate of convergence. It shows that the general nonparametric results have a parametric counterpart in terms of which values of the power p are better able to identify parameters from either the continuous or jump part of the model.

Keywords:   jumps, power variations, certain moment functions, high-frequency trading, financial data, stochastic processes

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