A simple testing procedure for unit root and model specification

Tests for the joint null hypothesis of a unit root based on the components representation of a time series are developed. The proposed testing procedure is designed to detect a unit root as well as guide the practitioner regarding the specification of trend component of a time series. The limiting null distributions of the newly developed F-statistics are derived. Finite sample simulation evidence shows that the F-statistics maintain their size, and have power against the trend-break stationary alternative. The use of our methodology is illustrated through an empirical examination of the US–UK real exchange rate, the UK industrial production, and the UK CPI series.