Publication Type

Journal Article

Version

acceptedVersion

Publication Date

2-2026

Abstract

A general asymptotic theory is established for sample cross moments of nonstationary time series, allowing for long-range dependence and local unit roots. The theory provides a substantial extension of earlier results on nonparametric regression that include near-cointegrated nonparametric regression as well as spurious nonparametric regression. Many new models are covered by the limit theory, among which are functional coefficient regressions in which both regressors and the functional covariate are nonstationary. Simulations show finite sample performance matching well with the asymptotic theory and having broad relevance to applications, while revealing how dual nonstationarity in regressors and covariates raises sensitivity to bandwidth choice and the impact of dimensionality in nonparametric regression. An empirical example is provided involving climate data regression to assess Earth’s climate sensitivity to CO2, where nonstationarity is a prominent feature of both the regressors and covariates in the model. To our knowledge, this application is the first nonparametric empirical analysis to assess potential nonlinear impacts of CO2 on Earth’s climate while allowing for nonstationarity in both the regressors and covariates.

Keywords

Climate sensitivity, cointegration, functional coefficient, nonlinear regression, nonstationarity, spurious regression

Discipline

Econometrics | Environmental Sciences

Research Areas

Econometrics

Publication

Econometric Theory

First Page

1

Last Page

53

ISSN

0266-4666

Identifier

10.1017/S0266466626100358

Publisher

Cambridge University Press

Copyright Owner and License

Authors

Additional URL

https://doi.org/10.1017/S0266466626100358

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