Asymptotics of the principal components estimator of large factor models with weak factors and i.i.d. Gaussian noise.
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Onatski, A.
Abstract
We consider large factor models where factors' explanatory power does not strongly dominate the explanatory power of the idiosyncratic terms asymptotically. We find the first and second order asymptotics of the principal components estimator of such a weak factors as the dimensionality of the data and the number of observations tend to infinity proportionally. The principal components estimator is inconsistent but asymptotically normal.
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Large factor models, principal components, phase transition, weak factors, inconsistency, asymptotic distribution, Marčenko-Pastur law.