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Robust and Powerful Tests for Nonlinear Deterministic Components
Author(s) -
Astill Sam,
Harvey David I.,
Leybourne Stephen J.,
Taylor A. M. Robert
Publication year - 2015
Publication title -
oxford bulletin of economics and statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.131
H-Index - 73
eISSN - 1468-0084
pISSN - 0305-9049
DOI - 10.1111/obes.12079
Subject(s) - univariate , nonlinear system , series (stratigraphy) , mathematics , fourier series , fourier transform , sample (material) , power (physics) , power series , econometrics , mathematical analysis , statistics , multivariate statistics , physics , paleontology , quantum mechanics , biology , thermodynamics
We develop a test for the presence of nonlinear deterministic components in a univariate time series, approximated using a Fourier series expansion, designed to be asymptotically robust to the order of integration of the process and to any weak dependence present. We show that our proposed test has uniformly greater local asymptotic power than the existing tests of Harvey, Leybourne and Xiao (2010) when the shocks are I(1), identical local asymptotic power when the shocks are I(0), and also improved finite sample properties. We also consider the issue of determining the number of Fourier frequencies used to specify any nonlinear deterministic components.