TESTING FOR A UNIT-ROOT IN TIME-SERIES USING INSTRUMENTAL VARIABLE ESTIMATORS WITH PRETEST DATA BASED MODEL SELECTION

Pantula and Hall (1991) proposed instrumental variable based tests for a unit root in an ARMA(p + 1,q) time series under the assumption that (p,q) are known. In this paper we derive conditions under which the Pantula-Hall tests still converge to the Dickey-Fuller distributions when (p,q) are chosen from the data. We propose a simple residual based statistic which can be used to estimate (p,q) and derive conditions under which the asymptotic distribution of the ensuing unit root tests are unaffected by this method of choosing (p,q). We also compare the local power properties of a number of unit root tests.