Open Access
Translator Disclaimer
April 2001 Nonparametric estimation in null recurrent time series
Hans Arnfinn Karlsen, Dag Tjøstheim
Ann. Statist. 29(2): 372-416 (April 2001). DOI: 10.1214/aos/1009210546


We develop a nonparametric estimation theory in a nonstationary environment, more precisely in the framework of null recurrent Markov chains. An essential tool is the split chain, which makes it possible to decompose the times series under consideration into independent and identical parts. A tail condition on the distribution of the recurrence time is introduced. This condition makes it possible to prove weak convergence results for sums of functions of the process depending on a smoothing parameter. These limit results are subsequently used to obtain consistency and asymptotic normality for local density estimators and for estimators of the conditional mean and the conditional variance. In contradistinction to the parametric case, the convergence rate is slower than in the stationary case, and it is directly linked to the tail behavior of the recurrence time. Applications to econometric, and in particular to cointegration models, are indicated.


Download Citation

Hans Arnfinn Karlsen. Dag Tjøstheim. "Nonparametric estimation in null recurrent time series." Ann. Statist. 29 (2) 372 - 416, April 2001.


Published: April 2001
First available in Project Euclid: 24 December 2001

zbMATH: 1103.62335
MathSciNet: MR1863963
Digital Object Identifier: 10.1214/aos/1009210546

Primary: 62G07 , 62M10
Secondary: 60J05

Keywords: nonparametric kernel estimators , Nonstationary time series models , null recurrent Markov chain , split chain

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.29 • No. 2 • April 2001
Back to Top