Johansen test with Fourier-type smooth nonlinear trends in cointegrating relations
提出在向量自回归模型的协整关系中引入傅里叶型平滑非线性趋势，推导了似然比检验统计量的极限分布并给出临界值，通过蒙特卡洛模拟评估了序贯选择协整秩的方法，实证表明该方法在经济数据中有效。
.We develop a methodology for testing the cointegrating rank in vector autoregressive (VAR) models in the presence of Fourier-type smooth nonlinear deterministic trends in cointegrating relations. The limiting distribution of log-likelihood ratio test statistics is derived, and approximate limit quantiles are tabulated. A sequential procedure to select the cointegrating rank is evaluated by Monte Carlo simulations. Our empirical application to economic data also demonstrates the usefulness of the proposed methodology in a practical context.