Revisiting Asymptotic Theory for Principal Component Estimators of Approximate Factor Models
1 November 2023
Shows existence of pseudo-true rotation for approximate factor models
Proves consistency of PC estimators for pseudo-true parameters
Derives asymptotic normality of PC estimators
Allows for weak factor models with differing strength
Applies approach to factor augmented regressions
Principal components for approximate factor models
This paper explores what the principal component estimators actually estimate for approximate factor models. It shows that under mild assumptions, the model can be rotated to a pseudo-true version that is separately identifiable. The paper proves consistency and asymptotic normality of the estimators relative to this pseudo-true parameter.
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