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Efficient inference for autoregressive coefficients in the presence of trends

Author

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  • Qiu, D.
  • Shao, Q.
  • Yang, L.

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.

Suggested Citation

  • Qiu, D. & Shao, Q. & Yang, L., 2013. "Efficient inference for autoregressive coefficients in the presence of trends," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 40-53.
    • Handle: RePEc:eee:jmvana:v:114:y:2013:i:c:p:40-53
    DOI: 10.1016/j.jmva.2012.07.016
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    References listed on IDEAS

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    1. L. Yang & R. Tschernig, 1999. "Multivariate bandwidth selection for local linear regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 793-815.
    2. Peter Hall & Ingrid Van Keilegom, 2003. "Using difference‐based methods for inference in nonparametric regression with time series errors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 443-456, May.
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    Cited by:

    1. Zhong, Chen, 2024. "Oracle-efficient estimation and trend inference in non-stationary time series with trend and heteroscedastic ARMA error," Computational Statistics & Data Analysis, Elsevier, vol. 193(C).
    2. L. Tang & Q. Shao, 2014. "Efficient Estimation For Periodic Autoregressive Coefficients Via Residuals," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(4), pages 378-389, July.
    3. Chen Zhong, 2025. "Simultaneous inference and trend specification testing in ARMA model with trend via innovation distribution function," Statistical Papers, Springer, vol. 66(5), pages 1-24, August.
    4. Qi Zheng & Yunwei Cui & Rongning Wu, 2024. "On estimation of nonparametric regression models with autoregressive and moving average errors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(2), pages 235-262, April.
    5. Benny Ren & Ian Barnett, 2022. "Autoregressive mixture models for clustering time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(6), pages 918-937, November.
    6. Qin Shao & Lijian Yang, 2017. "Oracally efficient estimation and consistent model selection for auto-regressive moving average time series with trend," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 507-524, March.

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