COINTEGRATION IN LARGE VARS

• 成果类型: Article
• 署名作者: Bykhovskaya, Anna; Gorin, Vadim
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/21-AOS2164
• 发表日期: 2022
• 页码: 1593-1617
• 关键词: largest eigenvalue; MULTIVARIATE-ANALYSIS; rank; tests; UNIVERSALITY; asymptotics; ensembles; spectrum; matrices; vectors

摘要

The paper analyzes cointegration in vector autoregressive processes (VARs) for the cases when both the number of coordinates, N, and the number of time periods, T, are large and of the same order. We propose a way to examine a VAR of order 1 for the presence of cointegration based on a modification of the Johansen likelihood ratio test. The advantage of our procedure over the original Johansen test and its finite sample corrections is that our test does not suffer from overrejection. This is achieved through novel asymptotic theorems for eigenvalues of matrices in the test statistic in the regime of proportionally growing N and T. Our theoretical findings are supported by Monte Carlo simulations and an empirical illustration. Moreover, we find a surprising connection with multivariate analysis of variance (MANOVA) and explain why it emerges.