Estimation of the bias parameter of the skew random walk and application to the skew Brownian motion

Antoine Lejay ()
Additional contact information
Antoine Lejay: Université de Lorraine, IECL, UMR 7502

Statistical Inference for Stochastic Processes, 2018, vol. 21, issue 3, No 4, 539-551

Abstract: Abstract We study the asymptotic property of simple estimator of the parameter of a skew Brownian motion when one observes its positions on a fixed grid—or equivalently of a simple random walk with a bias at 0. This estimator, nothing more than the maximum likelihood estimator, is based only on the number of passages of the random walk at 0. It is very simple to set up, is consistent and is asymptotically mixed normal. We believe that this simplified framework is helpful to understand the asymptotic behavior of the maximum likelihood of the skew Brownian motion observed at discrete times which is studied in a companion paper.

Keywords: Skew random walk; Skew Brownian motion; Maximum likelihood estimator; Local asymptotic mixed normality; Local time; Null recurrent process (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11203-017-9161-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sistpr:v:21:y:2018:i:3:d:10.1007_s11203-017-9161-9

Ordering information: This journal article can be ordered from
http://www.springer. ... ty/journal/11203/PS2

DOI: 10.1007/s11203-017-9161-9

Access Statistics for this article

Statistical Inference for Stochastic Processes is currently edited by Denis Bosq, Yury A. Kutoyants and Marc Hallin

More articles in Statistical Inference for Stochastic Processes from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().