Testing for Flexible Nonlinear Trends with an Integrated or Stationary Noise Component
Testing for Flexible Nonlinear Trends with an Integrated or Stationary Noise Component
复制标题
使用集成或固定噪声组件测试灵活的非线性趋势
DOI：
10.1111/obes.12169
复制
发表时间：
2017
影响因子：
2.5
通讯作者：
Mototsugu Shintani and Tomoyoshi Yabu
中科院分区：
文献类型：
--
作者：
Perron;Pierre;Mototsugu Shintani and Tomoyoshi Yabu
本文提出了一种新的测试存在的非线性确定性的趋势近似的傅立叶展开在一个单变量的时间序列，没有先验知识的噪声分量是否是平稳的或包含自回归单位根。我们的方法建立在Perron和Yabu（）的工作基础上，并且基于可行广义最小二乘过程，该过程使用自回归系数α之和的超有效估计，当α= 1时。由此产生的Wald检验统计量在I（0）和I（1）两种情况下都渐近遵循卡方分布。为了改善检验的有限样本性质，我们使用Roy和Fuller（）提出的α的OLS估计量的偏差校正版本。我们表明，我们的程序是更强大的比目前可用的替代品。我们说明了我们的方法的有用性，通过应用程序来模拟全球和半球温度的趋势。
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 coefficientsαwhenα= 1. The resulting Wald test statistic asymptotically follows a chi‐square distribution in both theI(0) andI(1) cases. To improve the finite sample properties of the test, we use a bias‐corrected version of the OLS estimator ofαproposed 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.