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Fisher's Information for Discretely Sampled Lévy Processes
Author(s) -
AïtSahalia Yacine,
Jacod Jean
Publication year - 2008
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.1111/j.1468-0262.2008.00858.x
Subject(s) - fisher information , estimator , mathematics , convergence (economics) , econometrics , lévy process , statistics , mathematical economics , statistical physics , economics , physics , economic growth
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.