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The impact of the initial condition on robust tests for a linear trend
Author(s) -
Harvey David I.,
Leybourne Stephen J.,
Robert Taylor A. M.
Publication year - 2010
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2010.00664.x
Subject(s) - univariate , mathematics , series (stratigraphy) , sensitivity (control systems) , statistics , econometrics , magnitude (astronomy) , multivariate statistics , paleontology , physics , astronomy , electronic engineering , engineering , biology
This article examines the behaviour of some recently proposed ‘robust’ (to the order of integration of the data) tests for the presence of a deterministic linear trend in a univariate times series in situations where the magnitude of the initial condition of the series is non‐negligible. We demonstrate that the asymptotic size and/or local power properties of these tests are extremely sensitive to the initial condition. Straightforward modifications to the trend tests are suggested, based on the use of trimmed data, which are shown to help reduce this sensitivity.