Efficient inference for autoregressive coefficients in the presence of trends

  • Authors:

  • D. Qiu;Q. Shao;L. Yang

  • Affiliations:

  • Soochow University, Suzhou, 215006, China;University of Toledo, Toledo, OH 43606, USA;Soochow University, Suzhou, 215006, China and Michigan State University, East Lansing, MI 48824, USA

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2013

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Abstract

Time series often contain unknown trend functions and unobservable error terms. As is known, Yule-Walker estimators are asymptotically efficient for autoregressive time series. The focus of this article is the Yule-Walker estimators for time series with trends. A nonparametric detrending procedure is proposed. It is concluded that the asymptotic properties of the Yule-Walker estimators of autoregressive coefficients are not altered by the detrending procedure. The results of the simulation studies and real data application corroborate the asymptotic theory.