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Testing for Flexible Nonlinear Trends with an Integrated or Stationary Noise Component
Author(s) -
Perron Pierre,
Shintani Mototsugu,
Yabu Tomoyoshi
Publication year - 2017
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.12169
Subject(s) - autoregressive model , estimator , mathematics , unit root , univariate , wald test , series (stratigraphy) , component (thermodynamics) , statistic , noise (video) , asymptotic distribution , test statistic , statistical hypothesis testing , nonlinear system , statistics , econometrics , computer science , multivariate statistics , artificial intelligence , paleontology , physics , quantum mechanics , image (mathematics) , biology , thermodynamics
This paper proposes a new test for the presence of a nonlinear deterministic trend approximated by a Fourier expansion in a univariate time series for which there is no prior knowledge as to whether the noise component is stationary or contains an autoregressive unit root. Our approach builds on the work of Perron and Yabu ([Perron, P., 2009a]) and is based on a Feasible Generalized Least Squares procedure that uses a super‐efficient estimator of the sum of the autoregressive coefficients α when α = 1. The resulting Wald test statistic asymptotically follows a chi‐square distribution in both the I (0) and I (1) cases. To improve the finite sample properties of the test, we use a bias‐corrected version of the OLS estimator of α proposed by Roy and Fuller ([Roy, A., 2001]). We show that our procedure is substantially more powerful than currently available alternatives. We illustrate the usefulness of our method via an application to modelling the trend of global and hemispheric temperatures.