Fisher's Information for Discretely Sampled Lévy Processes

By Yacine Aït-Sahalia, Jean Jacod. 2004

90 citations recorded by the source corpus.

This paper studies the asymptotic behavior of Fisher's information for a Levy 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. Copyright Copyright 2008 by The Econometric Society.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/d730786efc7cf62f690e9917296dfea4fbf312c2

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Citations in the corpus

Efficient Minimum Distance Estimation with Multiple Rates of Convergence (2012, background): “Aït-Sahalia and Jacod (2008) show that considering more generally Levy-stable processes introduces even more non-standard rates for jumps components and tails parameters.”
Estimation of Stable Distributions by Indirect Inference (2011, unknown): “Stable processes have recently been used in the high-frequency microstructure literature as well as in consumption-based equilibrium asset pricing models.(2)”
Local asymptotic normality for normal inverse Gaussian Lévy processes with high-frequency sampling (2010, methodology): “Also, Jacod [9] presents a nice concise review in this direction, with a particular focus on the case of diffusion processes.”
Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics (2008, methodology): “For an application of Edgeworth expansion in the context of realized volatility, see Zhang, Mykland, and A¨ıt-Sahalia (2005a).”
Convergence of Gaussian quasi-likelihood random fields for ergodic Lévy driven SDE observed at high frequency (2013, unknown): “Applying the Lenglart domination property for the martingale ∑n j=1(ηj − E j−1 0 [ηj ]) (cf. Jacod and Shiryaev [15], I.3.30), we conclude that ∑n j=1 ηj →p Vαβ[v′1, v′′1 ], hence V̂αβ,n[v′1, v′′1 ] →p Vαβ [v′1, v′′1 ].”
Volatility estimators for discretely sampled Lévy processes (2007, background): “In this paper, we focus on a single parameter, σ . In a companion paper, [ 2 ], we study the optimal rate at which other parameters of the model, namely β and a scale parameter θ for the Y process, can be estimated.”