Contrast function estimation for the drift parameter of ergodic jump diffusion process
| Autor: | Chiara Amorino, Arnaud Gloter |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), ENSIIE-Université d'Évry-Val-d'Essonne (UEVE)-Institut National de la Recherche Agronomique (INRA)-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Jump diffusion Mathematics - Statistics Theory Statistics Theory (math.ST) ergodic properties 01 natural sciences Lévy process thresholding methods 010104 statistics & probability [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] 0502 economics and business FOS: Mathematics Ergodic theory 0101 mathematics 050205 econometrics Mathematics Levy processes 05 social sciences Mathematical analysis Estimator high frequency SDE with jumps Thresholding Arbitrarily large Diffusion process Jump Efficient drift estimation Mathematics [G03] [Physical chemical mathematical & earth Sciences] Mathématiques [G03] [Physique chimie mathématiques & sciences de la terre] Statistics Probability and Uncertainty |
| Popis: | In this paper we consider an ergodic diffusion process with jumps whose drift coefficient depends on an unknown parameter $\theta$. We suppose that the process is discretely observed at the instants (t n i)i=0,...,n with $\Delta$n = sup i=0,...,n--1 (t n i+1 -- t n i) $\rightarrow$ 0. We introduce an estimator of $\theta$, based on a contrast function, which is efficient without requiring any conditions on the rate at which $\Delta$n $\rightarrow$ 0, and where we allow the observed process to have non summable jumps. This extends earlier results where the condition n$\Delta$ 3 n $\rightarrow$ 0 was needed (see [10],[24]) and where the process was supposed to have summable jumps. Moreover, in the case of a finite jump activity, we propose explicit approximations of the contrast function, such that the efficient estimation of $\theta$ is feasible under the condition that n$\Delta$ k n $\rightarrow$ 0 where k > 0 can be arbitrarily large. This extends the results obtained by Kessler [15] in the case of continuous processes. L{\'e}vy-driven SDE, efficient drift estimation, high frequency data, ergodic properties, thresholding methods. |
| Databáze: | OpenAIRE |
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