A surveillance procedure for random walks based on local linear estimation

Ansgar Steland

Journal of Nonparametric Statistics, 2010, vol. 22, issue 3, 345-361

Abstract: We study the problem of detecting a change in the trend of time series whose stochastic part behaves as a random walk. Interesting applications in finance and engineering come to mind. Local linear estimation provides a well established approach to estimating level and derivative of an underlying trend function, provided the time instants where observations are available become dense asymptotically. Here we study the local linear estimation principle for the classic time series setting where the distance between time points is fixed. It turns out that local linear estimation is applicable to the detection problem, and we identify the underlying (asymptotic) parameters. Assuming that observations arrive sequentially, we propose surveillance procedures and establish the relevant asymptotic theory, particularly, an invariance principle for the sequential empirical local linear process. A simulation study illustrates the remarkable accuracy of the approximations obtained by our asymptotics even in small samples as well as the excellent detection performance of the proposed surveillance procedure.

Date: 2010
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/10485250903082414 (text/html)
Access to full text is restricted to subscribers.

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:taf:gnstxx:v:22:y:2010:i:3:p:345-361

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/GNST20

DOI: 10.1080/10485250903082414

Access Statistics for this article

Journal of Nonparametric Statistics is currently edited by Jun Shao

More articles in Journal of Nonparametric Statistics from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().