Testing for flexible nonlinear trends with an integrated or stationary noise component
Files
Accepted manuscript
Date
2017-10-01
Authors
Perron, Pierre
Shintani, Mototsugu
Yabu, Tomoyoshi
Version
OA Version
Citation
Pierre Perron, Mototsugu Shintani, Tomoyoshi Yabu. 2017. "Testing for Flexible Nonlinear Trends with an Integrated or Stationary Noise Component." OXFORD BULLETIN OF ECONOMICS AND STATISTICS, Volume 79, Issue 5, pp. 822 - 850 (29).
Abstract
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 (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 (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.