Econometrica

Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Jul, 2008, Volume 76, Issue 4

Fisher's Information for Discretely Sampled Lévy Processes

https://doi.org/10.1111/j.1468-0262.2008.00858.x
p. 727-761

Yacine Aït‐Sahalia, Jean Jacod

This paper studies the asymptotic behavior of Fisher's information for a Lévy process discretely sampled at an increasing frequency. As a result, we derive the optimal rates of convergence of efficient estimators of the different parameters of the process and show that the rates are often nonstandard and differ across parameters. We also show that it is possible to distinguish the continuous part of the process from its jumps part, and even different types of jumps from one another.


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