Robust testing of time trend and mean with unknown integration order errors
Files
Accepted manuscript
Date
2022
Authors
Chang, Seong Yeon
Perron, Pierre
Xu, Jiawen
Version
Accepted manuscript
OA Version
Citation
S.Y. Chang, P. Perron, J. Xu. 2022. "Robust testing of time trend and mean with unknown integration order errors" Journal of Statistical Computation and Simulation, Volume 92, Issue 17, pp.3561-3582. https://doi.org/10.1080/00949655.2022.2074420
Abstract
We provide tests to perform inference on the coeโcient of a linear trend assuming
the noise to be a fractionally integrated process with memory parameter ๐ โ (โ0.5; 1.5)
excluding the boundary case 0.5 by applying a quasi-generalized least squares procedure
using ๐-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. To have feasible tests, we use the
exact local whittle estimator, valid for processes with a linear trend. The small sample
properties of the tests are investigated via simulations and we provide comparisons with
existing tests valid for a short-memory stationary, ๐ผ (0), or an autoregressive unit root, ๐ผ (1),
noise. The results are encouraging in that our test is valid under more general conditions,
yet has power approaching to the Perron and Yabu [Estimating deterministic trends with
an integrated or stationary noise component. J. of Econometrics. 2009;151;56-69] tests that
apply to the dichotomous cases with d either being 0 or 1. We also use our method of proof
to show that the main result of Iacone, Leybourne and Taylor [Testing for a break in trend
when the order of integration is unknown. J. of Econometrics. 2013;176:30-45] dealing with
a test for a break in the slope of a trend function with a fractionally integrated noise is
valid for ๐ โ (โ0.5) โช (0:5; 1:5).