Emily Whitehouse (University of Nottingham)

 Testing for a unit root against ESTAR stationarity (with D.I. Harvey and S.J. Leybourne)

 Abstract:   In this paper we examine the local power of unit root tests against globally stationary exponential smooth transition autoregressive [ESTAR] alternatives under two sources of uncertainty: the degree of nonlinearity in the ESTAR model, and the presence of a linear deterministic trend. First, we show that the Kapetanios et al. (2003, Journal of Econometrics 112, 359--379) [KSS] test for nonlinear stationarity has local asymptotic power gains over standard Dickey-Fuller [DF] tests for certain degrees of nonlinearity in the ESTAR model, but that for other degrees of nonlinearity, the linear DF test has superior power performance. Second, we derive limiting distributions of demeaned, and demeaned and detrended KSS and DF tests under a local ESTAR alternative when a local trend is present in the DGP. We show that the power of the demeaned tests outperforms that of the detrended tests when no trend is present in the DGP, but deteriorates as the magnitude of the trend increases. We propose a union of rejections testing procedure that combines all four individual tests and show that this captures most of the power available from the individual tests across different degrees of nonlinearity and trend magnitudes. We also show that incorporating a trend detection procedure into this union testing strategy can result in higher power when a large trend is present in the DGP. An empirical application of our proposed union of rejections procedures to energy consumption data in 180 countries shows the value of these tests in practice.