Estimating and testing high dimensional factor models with multiple structural changes

Abstract

This paper considers multiple changes in the factor loadings of a high dimensional factor model occurring at dates that are unknown but common to all subjects. Since the factors are unobservable, the problem is converted to estimating and testing structural changes in the second moments of the pseudo factors. We consider both joint and sequential estimation of the change points and show that the distance between the estimated and the true change points is O p (1). We …nd that the estimation error contained in the estimated pseudo factors has no e¤ect on the asymptotic properties of the estimated change points as the cross-sectional dimension N and the time dimension T go to in…nity jointly. No N -T ratio condition is needed. We also propose (i) tests for the null of no change versus the alternative of l changes (ii) tests for the null of l changes versus the alternative of l + 1 changes, and show that using estimated factors asymptotically has no e¤ect on their limit distributions if p T =N ! 0. These tests allow us to make inference on the presence and number of structural changes. Simulation results show good performance of the proposed procedure. In an application to US quarterly macroeconomic data we detect two possible breaks.

Instrumental-variable estimation of large-T panel-data models with common factors

“…The common factor approach is highly popular among panel-data practitioners because it offers a wide scope for controlling for omitted variables and rich sources of unobserved heterogeneity, including models with cross-sectional dependence; see, for example, Chudik and Pesaran (2015), Juodis and Sarafidis (2018), and Wansbeek (2012, 2021).…”

Tuning-Free Testing of Factor Regression Against Factor-Augmented Sparse Alternatives

“…Second, our work is related to the literature on tests for the factor regression model. Many papers test the validity of the factor model itself (the second equation in (1))(Breitung & Eickmeier (2011),Chen et al (2014),Han & Inoue (2015),Yamamoto & Tanaka (2015),Su & Wang (2017, 2020,Baltagi et al (2021),Xu (2022),Fu et al (2023)) whileCorradi & Swanson (2014) focuses on the factor regression model.In all these papers, the alternative hypothesis is that of the presence of structural breaks and/or smoothly time-varying loadings. Our approach complements this literature by proposing a specification test of the factor regression model under a different alternative, namely the factor-augmented sparse regression model.…”