Robust testing of time trend and mean with unknown integration order errors

Abstract

ABSTRACT We provide tests to perform inference on the coefficient of a linear trend assuming the noise to be a fractionally integrated process with memory parameter excluding the boundary case 0.5 by applying a quasi-generalized least-squares procedure using d-differences of the data. Doing so, the asymptotic distribution of the ordinary least-squares estimators applied to quasi-differenced data and their t-statistics are unaffected by the value of d and have a normal limiting distribution. We present simulation results about the size and power of the tests in finite samples and illustrate their usefulness via applications to the US equity indices. We also use our method of proof to consider generalizing the main result of Iacone, Leybourne and Taylor [Testing for a break in trend when the order of integration is unknown. J Econom. 2013;176:30–45] for .