Testing Hypotheses About the Number of Factors in Large Factor Models

Alexei Onatski

Econometrica, 2009, vol. 77, issue 5, pages 1447-1479

Abstract: In this paper we study high-dimensional time series that have the generalized dynamic factor structure. We develop a test of the null of k₀ factors against the alternative that the number of factors is larger than k₀ but no larger than k₁>k₀. Our test statistic equals max_k0>k⩽k1(Gamma_k - Gamma_k+1)(Gamma_k+1 - Gamma_k+2), where Gamma_i is the ith largest eigenvalue of the smoothed periodogram estimate of the spectral density matrix of data at a prespecified frequency. We describe the asymptotic distribution of the statistic, as the dimensionality and the number of observations rise, as a function of the Tracy-Widom distribution and tabulate the critical values of the test. As an application, we test different hypotheses about the number of dynamic factors in macroeconomic time series and about the number of dynamic factors driving excess stock returns. Copyright 2009 The Econometric Society.

Date: 2009

Downloads: (external link)
http://hdl.handle.net/10.3982/ECTA6964 link to full text (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: http://EconPapers.repec.org/RePEc:ecm:emetrp:v:77:y:2009:i:5:p:1447-1479

Ordering information: This journal article can be ordered from
http://www.blackwell ... mb.asp?ref=0012-9682

Access Statistics for this article

Econometrica is edited by Stephen Morris

More articles in Econometrica from Econometric Society
Contact information at EDIRC.
Series data maintained by Christopher F. Baum ().