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A weighted sieve estimator for nonparametric time series models with nonstationary variables

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  • Dong, Chaohua
  • Linton, Oliver
  • Peng, Bin

Abstract

We study a class of nonparametric regression models that includes deterministic time trends and both stationary and nonstationary stochastic processes (whose shocks are allowed to be mutually correlated). We propose a unified approach to estimation based on the weighted sieve method to tackle the issue of unbounded support of the covariates. This approach improves on the existing technology in terms of some key regularity conditions such as moment conditions and the α-mixing coefficients for the stationary process. We establish self-normalized central limit theorems for the sieve estimator and other related quantities. Monte Carlo simulation confirms the theoretical results. We use our methodology to study the effect of CO2 and solar irradiance on global sea level rise.

Suggested Citation

  • Dong, Chaohua & Linton, Oliver & Peng, Bin, 2021. "A weighted sieve estimator for nonparametric time series models with nonstationary variables," Journal of Econometrics, Elsevier, vol. 222(2), pages 909-932.
  • Handle: RePEc:eee:econom:v:222:y:2021:i:2:p:909-932
    DOI: 10.1016/j.jeconom.2020.03.024
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    Citations

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    Cited by:

    1. Tingting Cheng & Chaohua Dong & Jiti Gao & Oliver Linton, 2022. "GMM Estimation for High-Dimensional Panel Data Models," Monash Econometrics and Business Statistics Working Papers 11/22, Monash University, Department of Econometrics and Business Statistics.
    2. Christis Katsouris, 2023. "High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods," Papers 2308.16192, arXiv.org.
    3. Dong, C. & Li, S., 2021. "Specification Lasso and an Application in Financial Markets," Cambridge Working Papers in Economics 2139, Faculty of Economics, University of Cambridge.
    4. Dong, Chaohua & Gao, Jiti & Linton, Oliver, 2023. "High dimensional semiparametric moment restriction models," Journal of Econometrics, Elsevier, vol. 232(2), pages 320-345.
    5. Lin, Yingqian & Tu, Yundong, 2024. "Functional coefficient cointegration models with Box–Cox transformation," Economics Letters, Elsevier, vol. 234(C).
    6. Difang Huang & Jiti Gao & Tatsushi Oka, 2022. "Semiparametric Single-Index Estimation for Average Treatment Effects," Papers 2206.08503, arXiv.org, revised Apr 2024.
    7. Chaohua Dong & Jiti Gao & Bin Peng & Yundong Tu, 2021. "Multiple-index Nonstationary Time Series Models: Robust Estimation Theory and Practice," Monash Econometrics and Business Statistics Working Papers 18/21, Monash University, Department of Econometrics and Business Statistics.
    8. Peng, Zhen & Dong, Chaohua, 2022. "Augmented cointegrating linear models with possibly strongly correlated stationary and nonstationary regressors," Finance Research Letters, Elsevier, vol. 47(PB).
    9. Chaohua Dong & Jiti Gao & Bin Peng & Yundong Tu, 2021. "Multiple-index Nonstationary Time Series Models: Robust Estimation Theory and Practice," Papers 2111.02023, arXiv.org.

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    More about this item

    Keywords

    Nonparametric regression; Nonstationary variable; Sieve estimation; Stationary variable; Time trend; Unbounded support; Weighted least squares;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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