Is a Brownian Motion Skew?
Article first published online: 4 OCT 2013
© 2013 Board of the Foundation of the Scandinavian Journal of Statistics.
Scandinavian Journal of Statistics
Volume 41, Issue 2, pages 346–364, June 2014
How to Cite
Lejay, A., Mordecki, E. and Torres, S. (2014), Is a Brownian Motion Skew?. Scandinavian Journal of Statistics, 41: 346–364. doi: 10.1111/sjos.12033
- Issue published online: 6 MAY 2014
- Article first published online: 4 OCT 2013
- Manuscript Accepted: 23 APR 2013
- Manuscript Revised: 26 FEB 2013
- Manuscript Received: 10 DEC 2010
- maximum likelihood;
- skew Brownian motion;
- statistical estimation
We study the asymptotic behaviour of the maximum likelihood estimator corresponding to the observation of a trajectory of a skew Brownian motion, through a uniform time discretization. We characterize the speed of convergence and the limiting distribution when the step size goes to zero, which in this case are non-classical, under the null hypothesis of the skew Brownian motion being an usual Brownian motion. This allows to design a test on the skewness parameter. We show that numerical simulations can be easily performed to estimate the skewness parameter and provide an application in Biology.