New Asymptotics Applied to Functional Coefficient Regression and Climate Sensitivity Analysis

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 CO ₂ , 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 CO ₂ on Earth’s climate while allowing for nonstationarity in both the regressors and covariates.