Testing for Common Trends in Nonstationary Large Datasets
提出一种基于因子表示的检验程序，通过协方差矩阵特征值是否发散来判断大数据集中共同趋势的数量，适用于含线性趋势和随机趋势的因子，蒙特卡洛模拟显示有限样本性质良好，并应用于美国债券收益率数据。
We propose a testing-based procedure to determine the number of common trends in a large nonstationary dataset. Our procedure is based on a factor representation, where we determine whether there are (and how many) common factors (i) with linear trends, and (ii) with stochastic trends. Cointegration among the factors is also permitted. Our analysis is based on the fact that those largest eigenvalues of a suitably scaled covariance matrix of the data corresponding to the common factor part diverge, as the dimension <i>N</i> of the dataset diverges, whilst the others stay bounded. Therefore, we propose a class of randomized test statistics for the null that the <i>p</i>th largest eigenvalue diverges, based directly on the estimated eigenvalue. The tests only requires minimal assumptions on the data-generating process. Monte Carlo evidence shows that our procedure has very good finite sample properties, clearly dominating competing approaches when no common trends are present. We illustrate our methodology through an application to the U.S. bond yields with different maturities observed over the last 30 years.