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

Chaohua Dong, Jiti Gao

Research output: Contribution to journalArticleResearchpeer-review

### 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.

Original language English 125-150 26 Econometric Reviews 38 2 https://doi.org/10.1080/07474938.2016.1235305 Published - 2019

### Keywords

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

### Cite this

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title = "Expansion and estimation of L{\'e}vy process functionals in nonlinear and nonstationary time series regression",
abstract = "In this article, we develop a series estimation method for unknown time-inhomogeneous functionals of L{\'e}vy 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.",
keywords = "Asymptotic theory, L{\'e}vy process, orthogonal series expansion, series estimation, time-inhomogeneous functional",
author = "Chaohua Dong and Jiti Gao",
year = "2019",
doi = "10.1080/07474938.2016.1235305",
language = "English",
volume = "38",
pages = "125--150",
journal = "Econometric Reviews",
issn = "0747-4938",
publisher = "Taylor & Francis",
number = "2",

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In: Econometric Reviews, Vol. 38, No. 2, 2019, p. 125-150.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Expansion and estimation of Lévy process functionals in nonlinear and nonstationary time series regression

AU - Dong, Chaohua

AU - Gao, Jiti

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Asymptotic theory

KW - Lévy process

KW - orthogonal series expansion

KW - series estimation

KW - time-inhomogeneous functional

UR - http://www.scopus.com/inward/record.url?scp=84997611197&partnerID=8YFLogxK

U2 - 10.1080/07474938.2016.1235305

DO - 10.1080/07474938.2016.1235305

M3 - Article

VL - 38

SP - 125

EP - 150

JO - Econometric Reviews

JF - Econometric Reviews

SN - 0747-4938

IS - 2

ER -