Article2008

Fisher's Information for Discretely Sampled Lvy Processes

72 citations0/0 files storedEconometrica

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Stochastic processes and financial applications Probability and Statistical Research Financial Risk and Volatility Modeling

Abstract

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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References

1965The Behavior of Stock-Market Prices 1997The variation of certain speculative prices 2003Modeling and Forecasting Realized Volatility 2003Limit Theorems for Stochastic Processes 2004Power and Bipower Variation with Stochastic Volatility and Jumps 2002The Fine Structure of Asset Returns: An Empirical Investigation 1997Processes of normal inverse Gaussian type 1997Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling

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