Chang, Seong YeonPerron, PierreXu, Jiawen2024-06-052024-06-052022S.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/10.1080/00949655.2022.20744200094-96551563-5163https://hdl.handle.net/2144/48981We provide tests to perform inference on the coe cient of a linear trend assuming the noise to be a fractionally integrated process with memory parameter 𝑑 ∈ (−0.5; 1.5) 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. 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, 𝐼 (0), or an autoregressive unit root, 𝐼 (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 𝑑 ∈ (—0.5) ∪ (0:5; 1:5).p. 3561-3582enConfidence intervalsFractional integrationInferenceLinear time trendLong memoryQuasi-GLS procedurecon- Ödence intervalsStatisticsApplied economicsEconometricsStatistics & probabilityArticle2024-02-0110.1080/00949655.2022.2074420120507