Testing for Common Trends in Nonstationary Large Datasets

Barigozzi, Matteo; Trapani, Lorenzo

Abstract

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 N of the dataset diverges, whilst the others stay bounded. Therefore, we propose a class of randomized test statistics for the null that the pth 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.

Citation

Barigozzi, M., & Trapani, L. (2022). Testing for Common Trends in Nonstationary Large Datasets. Journal of Business and Economic Statistics, 40(3), 1107-1122. https://doi.org/10.1080/07350015.2021.1901719

• Journal Article Type: Article
• Acceptance Date: Mar 5, 2021
• Online Publication Date: Apr 21, 2021
• Publication Date: 2022
• Deposit Date: Mar 9, 2021
• Publicly Available Date: Apr 22, 2022
• Journal: Journal of Business and Economic Statistics
• Print ISSN: 0735-0015
• Electronic ISSN: 1537-2707
• Publisher: Taylor and Francis
• Peer Reviewed: Peer Reviewed
• Volume: 40
• Issue: 3
• Pages: 1107-1122
• DOI: https://doi.org/10.1080/07350015.2021.1901719
• Public URL: https://nottingham-repository.worktribe.com/output/5382234
• Publisher URL: https://www.tandfonline.com/doi/full/10.1080/07350015.2021.1901719
• Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Business & Economic Statistics on 11/03/21, available online: http://www.tandfonline.com/10.1080/07350015.2021.1901719