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Semiparametric Time Series Regression

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  • Young K. Truong
  • Charles J. Stone

Abstract

. Let (Xi, Yi), i= 0, pL 1,… denote a bivariate stationary time series with Xi being Rd‐valued and Yi being real‐valued. We consider the regression model Yi=θ(Xi) +Zi, where θ(·) is an unknown function and Zi is an autoregressive process. Given a realization of length n, we examine the problem of estimating the nonparametric function θ(·) and the parametric component Zi. Under appropriate regularity conditions, it is shown that both components can be optimally estimated.

Suggested Citation

  • Young K. Truong & Charles J. Stone, 1994. "Semiparametric Time Series Regression," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(4), pages 405-428, July.
  • Handle: RePEc:bla:jtsera:v:15:y:1994:i:4:p:405-428
    DOI: 10.1111/j.1467-9892.1994.tb00202.x
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    Cited by:

    1. Shao, Zhen & Gao, Fei & Zhang, Qiang & Yang, Shan-Lin, 2015. "Multivariate statistical and similarity measure based semiparametric modeling of the probability distribution: A novel approach to the case study of mid-long term electricity consumption forecasting i," Applied Energy, Elsevier, vol. 156(C), pages 502-518.
    2. Ip, Wai-Cheung & Wong, Heung & Li, Yuan & Xie, Zhongjie, 1999. "Threshold variable selection by wavelets in open-loop threshold autoregressive models," Statistics & Probability Letters, Elsevier, vol. 42(4), pages 375-392, May.
    3. Patrick Saart & Jiti Gao & Nam Hyun Kim, 2014. "Semiparametric methods in nonlinear time series analysis: a selective review," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 141-169, March.
    4. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    5. Wang, Qiao, 2023. "A simple nonparametric conditional quantile estimator for time series with thin tails," Economics Letters, Elsevier, vol. 232(C).
    6. Dursun Aydın & Ersin Yılmaz, 2021. "Semiparametric modeling of the right-censored time-series based on different censorship solution techniques," Empirical Economics, Springer, vol. 61(4), pages 2143-2172, October.

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