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

Jungbin Hwang and Yixiao Sun

No 2025-01, Working papers from University of Connecticut, Department of Economics

Abstract: 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.

Keywords: F test and F distribution; nonlinear cointegrating regression; unit root; t test and t distribution; fractional integration (search for similar items in EconPapers)
JEL-codes: C12 C13 C32 (search for similar items in EconPapers)
Pages: 43 pages
Date: 2025-01
New Economics Papers: this item is included in nep-ecm and nep-ets
Note: Jungbin Hwang is the corresponding author
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