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STS550 Pierre Guérin et al.

Markov-Switching three-pass regression filter
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2
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Pierre Guérin , Danilo Leiva-Leon , Massimiliano Marcellino
1 OECD
2 Banco de España
3 Bocconi University, IGIER and CEPR

Abstract
We introduce a new approach for the estimation of high-dimensional factor
models with regime-switching factor loadings by extending the linear three-pass
regression filter to settings where parameters can vary according to Markov
processes. The new method, denoted as Markov-switching three-pass regression
filter (MS-3PRF), is suitable for data sets with large cross-sectional dimensions,
since estimation and inference are straightforward. Both Monte Carlo simulations
and empirical applications show significant predictive gains when using the
proposed framework.

Keywords
Factor model; Markov-switching; Forecasting

1. Introduction
This paper introduces a new approach for the estimation of high-
dimensional factor models with regime-switching factor loadings. Our
modelling approach builds on Kelly and Pruitt (2015), who developed a new
estimator for factor models—the three-pass regression filter (3PRF)—that
relies on a series of ordinary least squares (OLS) regressions. As emphasized
in Kelly and Pruitt (2015), the key difference between principal component
analysis (PCA) and the 3PRF approach is that PCA summarizes the cross-
sectional information based on the covariance within the predictors, whereas
3PRF condenses cross-sectional information based on the correlation of the
predictors with the target variable of the forecasting exercise, thereby
extending partial least squares.
In this paper, we extend the 3PRF approach by introducing regime-
switching parameters in the linear 3PRF filter. This new framework is denoted
as Markov-switching three-pass regression filter (MS-3PRF). A key advantage
of this approach is that it is well suited to handle high-dimensional factor
models, as opposed to the existing regime-switching factor models that can
handle only models with limited dimensions due to computational com-
plexity (see, e.g., Camacho et al. (2012)). Our approach is attractive in that
the estimation strategy only requires estimating a series of univariate
Markov-switching regressions. As such, it is computationally straightforward

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