  Quantile feature selection over correlated multivariate time series data has
always been a methodological challenge and is an open problem. In this paper,
we propose a general Bayesian dimension reduction methodology for feature
selection in high-dimensional joint quantile time series analysis, under the
name of the quantile feature selection time series (QFSTS) model. The QFSTS
model is a general structural time series model, where each component yields an
additive contribution to the time series modeling with direct interpretations.
Its flexibility is compound in the sense that users can add/deduct components
for each time series and each time series can have its own specific valued
components of different sizes. Feature selection is conducted in the quantile
regression component, where each time series has its own pool of
contemporaneous external predictors allowing nowcasting. Bayesian methodology
in extending feature selection to the quantile time series research area is
developed using multivariate asymmetric Laplace distribution, spike-and-slab
prior setup, the Metropolis-Hastings algorithm, and the Bayesian model
averaging technique, all implemented consistently in the Bayesian paradigm. The
QFSTS model requires small datasets to train and converges fast. Extensive
examinations confirmed that the QFSTS model has superior performance in feature
selection, parameter estimation, and forecast.
