Spectral estimation of the fractional order of a Lévy process

Details Spectral estimation of the fractional order of a Lévy process Spectral estimation of the fractional order of a Lévy process

2010-01-12

arxiv.org/abs/1001.1820v1

Annals of Statistics 2010, Vol. 38, No. 1, 317-351

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/09-AOS715 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/09-AOS715

We consider the problem of estimating the fractional order of a L\'{e}vy process from low frequency historical and options data. An estimation methodology is developed which allows us to treat both estimation and calibration problems in a unified way. The corresponding procedure consists of two steps: the estimation of a conditional characteristic function and the weighted least squares estimation of the fractional order in spectral domain. While the second step is identical for both calibration and estimation, the first one depends on the problem at hand. Minimax rates of convergence for the fractional order estimate are derived, the asymptotic normality is proved and a data-driven algorithm based on aggregation is proposed. The performance of the estimator in both estimation and calibration setups is illustrated by a simulation study.

Affiliated with

Also associated with

No associations

Rating

Spectral estimation of the fractional order of a Lévy process does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Spectral estimation of the fractional order of a Lévy process, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spectral estimation of the fractional order of a Lévy process will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-459006