A1344
Title: Bayesian Markov-switching partial reduced-rank regression
Authors: Maria Fernanda Pintado - CUNEF Universidad (Spain) [presenting]
Matteo Iacopini - LUISS Guido Carli (Italy)
Luca Rossini - University of Milan (Italy)
Alexander Shestopaloff - Queen Mary University of London (United Kingdom)
Abstract: Reduced-rank (RR) regression is a powerful dimensionality reduction technique, but traditional RR models typically overlook any potential group structure among the responses by assuming a low-rank structure on the coefficient matrix. When the observations in the regression model are indexed by time, the relationship between covariates and responses could change over periods. A time-varying grouping structure in the response variables in RR regression is currently understudied. To address this limitation, a Markov-switching Bayesian partial RR (MSPRR) regression is proposed. First, the response vector is partitioned into two groups to reflect different degrees of complexity of the relationship. A "simple" group assumes a low-rank linear regression, and a "flexible" group remains agnostic and exploits nonparametric regression via a Gaussian process. Second, different from traditional approaches that assume known group structure and rank, they are treated as unknown parameters to be estimated. Third, time variation and persistence are accounted for by introducing a Markov-switching process, which examines the changes in the grouping structure and model parameters over time. Fully Bayesian inference is performed via a partially collapsed Gibbs sampler, which allows uncertainty quantification. Applications to both synthetic and macroeconomic data demonstrate the capability of the proposed method to uncover latent states and hidden structures within the data.
