An LM-type test for idiosyncratic unit roots in the exact factor model with integrated factors. Issue 10 (19th May 2017)

• Record Type: Journal Article
• Authors: Zhou, Xingwu; Solberger, Martin
• Is Part Of: Communications in statistics. Volume 46:Issue 10(2017)
• Page Start: 4888
• Page End: 4914
• Publication Date: 2017-05-19
• Subjects: Dynamic factors -- Lagrange multiplier -- Maximum likelihood -- Panel unit root.; C12 -- C23; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2015.1091079
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: We consider an exact factor model with integrated factors and propose an LM-type test for unit roots in the idiosyncratic component. We show that, for a fixed number of panel individuals ( N ) and when the number of time points ( T ) tends to infinity, the limiting distribution of the LM-type statistic is a weighted sum of independent Chi-square variables with one degree of freedom, and when T tends to infinity followed by N tending to infinity, the limiting distribution is standard normal. The results should contribute to the challenging task of deriving likelihood-based unit-root tests in dynamic factor models.