Asymptotic F and t Tests in Cointegrating Regressions with Asymptotically Homogeneous Functions

This paper develops asymptotic F and t tests for nonlinear cointegrated re-gression, where regressors are asymptotically homogeneous transformations of I(1) processes. These transformations encompass a broad class of functions, includ-ing distribution-like functions, logarithmic functions, and asymptotically polynomial functions. Our asymptotic F and t test theory covers both the case with exogenous regressors and the case with endogenous regressors. For the exogenous case, we con-struct a novel set of basis functions for series long-run variance estimation, effectively accounting for parameter estimation uncertainty. For the endogenous case, we extend the transformed-augmented OLS approach developed for linear cointegrated settings. Monte Carlo simulations show that our asymptotic F and t tests outperform compet-ing tests, including the asymptotic chi-square test based on the fully modified OLS estimator and the non-standard fixed-b test based on the integrated modified OLS estimator. Furthermore, our theory extends to cases where the processes driving regressors are nonstationary, fractionally integrated processes.