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

Chaohua Dong, Jiti Gao

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1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)125-150
Number of pages26
JournalEconometric Reviews
Issue number2
Publication statusPublished - 2019


  • Asymptotic theory
  • Lévy process
  • orthogonal series expansion
  • series estimation
  • time-inhomogeneous functional

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