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Expansion and estimation of Lévy process functionals in nonlinear and nonstationary time series regression

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  • Chaohua Dong
  • Jiti Gao

Abstract

In this article, we develop a series estimation method for unknown time-inhomogeneous functionals of Lévy processes involved in econometric time series models. To obtain an asymptotic distribution for the proposed estimators, we establish a general asymptotic theory for partial sums of bivariate functionals of time and nonstationary variables. These results show that the proposed estimators in different situations converge to quite different random variables. In addition, the rates of convergence depend on various factors rather than just the sample size. Finite sample simulations are provided to evaluate the finite sample performance of the proposed model and estimation method.

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  • Chaohua Dong & Jiti Gao, 2019. "Expansion and estimation of Lévy process functionals in nonlinear and nonstationary time series regression," Econometric Reviews, Taylor & Francis Journals, vol. 38(2), pages 125-150, February.
    • Handle: RePEc:taf:emetrv:v:38:y:2019:i:2:p:125-150
    DOI: 10.1080/07474938.2016.1235305
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    Cited by:

    1. 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.
    2. 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.
    3. 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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