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Additive nonparametric models with time variable and both stationary and nonstationary regressors

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  • Dong, Chaohua
  • Linton, Oliver

Abstract

This paper considers nonparametric additive models that have a deterministic time trend and both stationary and integrated variables as components. The diverse nature of the regressors caters for applications in a variety of settings. In addition, we extend the analysis to allow the stationary regressor to be instead locally stationary, and we allow the models to include a linear form of the integrated variable. Heteroscedasticity is allowed for in all models. We propose an estimation strategy based on orthogonal series expansion that takes account of the different type of stationarity/nonstationarity possessed by each covariate. We establish pointwise asymptotic distribution theory jointly for all estimators of unknown functions and also show the conventional optimal convergence rates jointly in the L2 sense. In spite of the entanglement of different kinds of regressors, we can separate out the distribution theory for each estimator. We provide Monte Carlo simulations that establish the favorable properties of our procedures in moderate sized samples. Finally, we apply our techniques to the study of a pairs trading strategy.

Suggested Citation

  • Dong, Chaohua & Linton, Oliver, 2018. "Additive nonparametric models with time variable and both stationary and nonstationary regressors," Journal of Econometrics, Elsevier, vol. 207(1), pages 212-236.
  • Handle: RePEc:eee:econom:v:207:y:2018:i:1:p:212-236
    DOI: 10.1016/j.jeconom.2018.05.007
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    1. Ruiqi Liu & Ben Boukai & Zuofeng Shang, 2019. "Statistical Inference on Partially Linear Panel Model under Unobserved Linearity," Papers 1911.08830, arXiv.org.
    2. Bin Peng & Liangjun Su & Joakim Westerlund & Yanrong Yang, 2021. "Interactive Effects Panel Data Models with General Factors and Regressors," Papers 2111.11506, arXiv.org.
    3. Fei Liu & Jiti Gao & Yanrong Yang, 2019. "Nonparametric Estimation in Panel Data Models with Heterogeneity and Time Varyingness," Monash Econometrics and Business Statistics Working Papers 24/19, Monash University, Department of Econometrics and Business Statistics.
    4. Chaohua Dong & Jiti Gao & Oliver Linton, 2017. "High dimensional semiparametric moment restriction models," Monash Econometrics and Business Statistics Working Papers 17/17, Monash University, Department of Econometrics and Business Statistics.
    5. Tingting Cheng & Jiti Gao & Oliver Linton, 2019. "Nonparametric Predictive Regressions for Stock Return Prediction," Monash Econometrics and Business Statistics Working Papers 4/19, Monash University, Department of Econometrics and Business Statistics.
    6. Bin Peng & Liangjun Su & Joakim Westerlund & Yanrong Yang, 2021. "Interactive Effects Panel Data Models with General Factors and Regressors," Monash Econometrics and Business Statistics Working Papers 23/21, Monash University, Department of Econometrics and Business Statistics.
    7. Lin, Yingqian & Tu, Yundong & Yao, Qiwei, 2020. "Estimation for double-nonlinear cointegration," Journal of Econometrics, Elsevier, vol. 216(1), pages 175-191.
    8. Guohua Feng & Jiti Gao & Bin Peng, 2019. "An Integrated Panel Data Approach to Modelling Economic Growth," Papers 1903.07948, arXiv.org.
    9. 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.
    10. Guohua Feng & Jiti Gao & Bin Peng, 2019. "An Integrated Panel Data Approach to Modelling Economic Growth," Monash Econometrics and Business Statistics Working Papers 6/19, Monash University, Department of Econometrics and Business Statistics.
    11. Feng, Guohua & Peng, Bin & Su, Liangjun & Yang, Thomas Tao, 2019. "Semi-parametric single-index panel data models with interactive fixed effects: Theory and practice," Journal of Econometrics, Elsevier, vol. 212(2), pages 607-622.
    12. 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.
    13. 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.

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    More about this item

    Keywords

    Additive nonparametric models; Deterministic trend; Pairs trading; Series estimator; Stationary and locally stationary processes; Unit root process;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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