We propose a new unit-root test for a stationary null hypothesis $H_0$ against a unit-root alternative $H_1$. Our approach is nonparametric as $H_0$ only assumes that the process concerned is $I(0)$ without specifying any parametric forms. The new test is based on the fact that the sample autocovariance function (ACVF) converges to the finite population ACVF for an $I(0)$ process while it diverges to infinity for a process with unit-roots. Therefore the new test rejects $H_0$ for the large values of the sample ACVF. To address the technical challenge `how large is large', we split the sample and establish an appropriate normal approximation for the null-distribution of the test statistic. The substantial discriminative power of the new test statistic is rooted from the fact that it takes finite value under $H_0$ and diverges to infinity under $H_1$. This allows us to truncate the critical values of the test to make it with the asymptotic power one. It also alleviates the loss of power due to the sample-splitting. The test is implemented in a user-friendly R-function.
Testing for functional white noise in high dimensions
Joint Laboratory of Data Science and Business Intelligence, Institute of Statistical Interdisciplinary Research, Southwestern University of Finance and Economics（西南财经大学统计交叉研究院数据科学与商业智能联合实验室）；State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院数学科学重点实验室）；China Center for Economic Research, Peking University（北京大学中国经济研究中心）；Faculty of Arts and Sciences, Beijing Normal University（北京师范大学文理学院）；Faculty of Business and Economics, The University of Hong Kong（香港大学工商管理学院）
Factor-Adjusted Location Tests for High-Dimensional Time Series
College of Mathematics and Systems Science, Xinjiang University（新疆大学数学与系统科学学院）；School of Mathematics, Yunnan Normal University（云南师范大学数学学院）；School of Statistics and Data Science, Nankai University（南开大学统计与数据科学学院）
