Factor-Driven Two-Regime Regression
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We propose a novel two-regime regression model where regime switching is driven by a vector of possibly unobservable factors. When the factors are latent, we estimate them by the principal component analysis of a panel data set. We show that the optimization problem can be reformulated as mixed integer optimization, and we present two alternative computational algorithms. We derive the asymptotic distribution of the resulting estimator under the scheme that the threshold effect shrinks to zero. In particular, we establish a phase transition that describes the effect of first-stage factor estimation as the cross-sectional dimension of panel data increases relative to the time-series dimension. Moreover, we develop bootstrap inference and illustrate our methods via numerical studies.
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Spurious regression analysis in panel data when the time series are cross-section dependent is analyzed in the article.The set-up includes (possibly unknown) multiple structural breaks that can affect both the deterministic and the common factor components.We show that consistent estimation of the long-run average parameter is possible once cross-section dependence is controlled using cross-section averages in the spirit of Pesaran's common correlated effects approach.This…
因子成分与特异成分的经验过程
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This paper studies large dimensional factor models with threshold-type regime shifts in the loadings. We estimate the threshold by concentrated least squares, and factors and loadings by principal components. The estimator for the threshold is superconsistent, with convergence rate that depends on the time and cross-sectional dimensions of the panel, and it does not affect the estimator for factors and loadings: this has the same convergence rate as in linear factor models.…