Abstract
As is well known, when using an information criterion to select the number of common factors in factor models the appropriate penalty is generally indetermine in the sense that it can be scaled by an arbitrary constant, c say, without affecting consistency. In an influential paper, Hallin and Liška (J Am Stat Assoc 102:603–617, 2007) proposes a data-driven procedure for selecting the appropriate value of c. However, by removing one source of indeterminacy, the new procedure simultaneously creates several new ones, which make for rather complicated implementation, a problem that has been largely overlooked in the literature. By providing an extensive analysis using both simulated and real data, the current paper fills this gap.
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Notes
See Pesaran (2006) for an alternative approach based on the cross-section averages of the observed data.
In their illustrative examples, Hallin and Liška (2007) use ocular inspection of graphs similar to Fig. 1 identify the second stability interval. But they do not describe in detail how the approach is operationalized in their Monte Carlo study. We experimented with a large number of alternative search schemes, but found that the one based on setting \(\hat{c}\) according to the second interval for which \(S_c^2 = 0\) tended to perform best. In this paper, we therefore only consider this scheme, which is the same as the one employed by Alessi et al. (2010).
This is in agreement with the results of Bai and Ng (2002) showing how \(IC_{p1}\) tend to underestimate \(r_0\) when N and/or T are “small”.
The data are available at http://www.princeton.edu/~mwatson/wp.html.
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Acknowledgments
The authors would like to thank Simon Svensson, Christine Müller (Editor) and two anonymous referees for their very constructive comments. Financial support from the Knut and Alice Wallenberg Foundation and the Jan Wallander and Tom Hedelius Foundation is gratefully acknowledged.
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Westerlund, J., Mishra, S. On the determination of the number of factors using information criteria with data-driven penalty. Stat Papers 58, 161–184 (2017). https://doi.org/10.1007/s00362-015-0692-0
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DOI: https://doi.org/10.1007/s00362-015-0692-0