Testing for Flexible Nonlinear Trends with an Integrated or Stationary Noise Component
提出一种新检验方法，用于判断单变量时间序列是否存在由傅里叶展开逼近的非线性确定性趋势，且无需事先知道噪声是平稳还是含单位根，通过可行广义最小二乘和偏差校正估计量提高检验功效。
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 ( ) 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 ( ). 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.