Testing Unit Root Based on Partially Adaptive Estimation

Abstract

This paper proposes unit root tests based on partially adaptive estimation. The proposed tests provide an intermediate class of inference procedures that are more efficient than the traditional OLS-based methods and simpler than unit root tests based on fully adaptive estimation using nonparametric methods. Taking into account the well documented characteristic of heavy-tail behavior in economic and financial data, we consider unit root tests coupled with a class of partially adaptive M-estimators based on the student-t distributions, which includes the normal distribution as a limiting case. Monte Carlo experiments indicate that, in the presence of heavy tail distributions, the proposed test is more powerful than the traditional ADF test. We apply the proposed test to several macroeconomic time series that have heavy-tailed distributions. The unit root hypothesis is rejected in U.S. real GNP, supporting the literature of transitory shocks in output. However, evidence against unit root is not found in real exchange rate and nominal interest rate even when heavy-tail is taken into account.