LOCAL LINEAR M-ESTIMATORS IN NULL RECURRENT TIME SERIES

Zhengyan Lin*, Degui Li, Jia Chen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we study a nonlinear cointegration type model Y(k) = m(X(k)) + w(k), where {Y(k)} and {X(k)} are observed nonstationary processes and {w(k)} is an unobserved stationary process. The process {X(k)} is assumed to be a null-recurrent Markov chain. We apply a robust version of local linear regression smoothers to estimate m(.). Under mild conditions, the uniform weak consistency and asymptotic normality of the local linear M-estimators are established. Furthermore, a one-step iterated procedure is introduced to obtain the local linear M-estimator and the optimal bandwidth selection is discussed. Meanwhile, some numerical examples are given to show that the proposed theory and methods perform well in practice.

Original languageEnglish
Pages (from-to)1683-1703
Number of pages21
JournalStatistica Sinica
Volume19
Issue number4
Publication statusPublished - Oct 2009

Keywords

  • BAHADUR REPRESENTATION
  • Asymptotic normality
  • consistency
  • local linear M-estimator
  • REGRESSION
  • beta-null recurrent Markov chain
  • NONPARAMETRIC-ESTIMATION
  • cointegration model

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