Abstract
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.
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