Open Access
2010 Parametric estimation for discretely observed stochastic processes with jumps
Hoang-Long Ngo
Electron. J. Statist. 4: 1443-1469 (2010). DOI: 10.1214/10-EJS590


We consider a two dimensional stochastic process (X,Y), which may have jump components and is not necessarily ergodic. There is an unknown parameter θ within the coefficients of (X,Y). The aim of this paper is to estimate θ from a regularly spaced sample of the process (X,Y). When the dynamic of X is known, an estimator is constructed by using a moment-based method. We show that our estimators will work if the Blumenthal-Getoor index of the jump part of Y is less than 2. What is perhaps the most interesting is the rate at which the estimators converge: it is $1/{\sqrt{n}}$ (as when the underlying processes are not contaminated by jumps) when that index is not greater than 1. When the dynamic of X is unknown, we introduce a spot volatility estimator-based approach to estimate θ. This approach can work even if the sample is contaminated by microstructure noise.


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Hoang-Long Ngo. "Parametric estimation for discretely observed stochastic processes with jumps." Electron. J. Statist. 4 1443 - 1469, 2010.


Published: 2010
First available in Project Euclid: 9 December 2010

zbMATH: 1329.62367
MathSciNet: MR2741208
Digital Object Identifier: 10.1214/10-EJS590

Primary: 60J75 , 60M09
Secondary: 60M05 , 62G05

Keywords: Blumenthal-Getoor index , discrete observation , jump process , microstructure noise , non-ergodic process , nonparameric estimation , Parametric estimation

Rights: Copyright © 2010 The Institute of Mathematical Statistics and the Bernoulli Society

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