More powerful modifications of unit root tests allowing structural change

Abstract

It is well known that more powerful variants of Dickey–Fuller unit root tests are available. We apply two of these modifications, on the basis of simple maximum statistics and weighted symmetric estimation, to Perron tests allowing for structural change in trend of the additive outlier type. Local alternative asymptotic distributions of the modified test statistics are derived, and it is shown that their implementation can lead to appreciable finite sample and asymptotic gains in power over the standard tests. Also, these gains are largely comparable with those from GLS-based modifications to Perron tests, though some interesting differences do arise. This is the case for both exogenously and endogenously chosen break dates. For the latter choice, the new tests are applied to the Nelson–Plosser data.

Keywords:

• Structural change
• Perron tests
• MAX test
• Weighted symmetric estimation
• GLS estimation
• Power comparison

Notes

^†Under the null c=0, the statistics are invariant to u ₀, hence we can fix u ₀=0 without loss of generality.

^‡Note that J _c (r)=W(r) when c=0.

^†We retain as the tests remain invariant to these parameters under the alternative c<0.

^†That this is also true for the GLS test is not surprising since it is constructed to be near optimal under the assumption that assuming u ₀ is fixed at the value 0, which is a condition that we do not impose here.