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Nonparametric estimation of a periodic sequence in the presence of a smooth trend

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  • Michael Vogt
  • Oliver Linton

Abstract

We investigate a nonparametric regression model including a periodic component, a smooth trend function, and a stochastic error term. We propose a procedure to estimate the unknown period and the function values of the periodic component as well as the nonparametric trend function. The theoretical part of the paper establishes the asymptotic properties of our estimators. In particular, we show that our estimator of the period is consistent. In addition, we derive the convergence rates and the limiting distributions of our estimators of the periodic component and the trend function. The asymptotic results are complemented with a simulation study and an application to global temperature anomaly data.

Suggested Citation

  • Michael Vogt & Oliver Linton, 2014. "Nonparametric estimation of a periodic sequence in the presence of a smooth trend," Biometrika, Biometrika Trust, vol. 101(1), pages 121-140.
    • Handle: RePEc:oup:biomet:v:101:y:2014:i:1:p:121-140.
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    Cited by:

    1. Michael Vogt & Oliver Linton, 2015. "Classification of nonparametric regression functions in heterogeneous panels," CeMMAP working papers CWP06/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Linton, Oliver & Wu, Jianbin, 2020. "A coupled component DCS-EGARCH model for intraday and overnight volatility," Journal of Econometrics, Elsevier, vol. 217(1), pages 176-201.
    3. Vogt, Michael & Linton, Oliver, 2020. "Multiscale clustering of nonparametric regression curves," Journal of Econometrics, Elsevier, vol. 216(1), pages 305-325.
    4. Peter Malec, 2016. "A Semiparametric Intraday GARCH Model," Cambridge Working Papers in Economics 1633, Faculty of Economics, University of Cambridge.
    5. Seok Young Hong & Oliver Linton & Hui Jun Zhang, 2014. "Multivariate variance ratio statistics," CeMMAP working papers CWP29/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Kai Yang & Peihua Qiu, 2022. "A three-step local smoothing approach for estimating the mean and covariance functions of spatio-temporal Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(1), pages 49-68, February.
    7. Koo, B. & La Vecchia, D. & Linton, O., 2019. "Nonparametric Recovery of the Yield Curve Evolution from Cross-Section and Time Series Information," Cambridge Working Papers in Economics 1916, Faculty of Economics, University of Cambridge.
    8. Koo, Bonsoo & La Vecchia, Davide & Linton, Oliver, 2021. "Estimation of a nonparametric model for bond prices from cross-section and time series information," Journal of Econometrics, Elsevier, vol. 220(2), pages 562-588.
    9. Liu, Jialuo & Chu, Tingjin & Zhu, Jun & Wang, Haonan, 2021. "Semiparametric method and theory for continuously indexed spatio-temporal processes," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    10. Marina Khismatullina & Michael Vogt, 2022. "Multiscale Comparison of Nonparametric Trend Curves," Papers 2209.10841, arXiv.org.

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