Probabilistic Feature Selection in Joint Quantile Time Series Analysis

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 probabilistic methodology for feature selection in joint quantile time series analysis, under the name of 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 times 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". Creative probabilistic methodology in extending feature selection to the quantile time series research area is developed by means of 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. Different from most machine learning algorithms, the QFSTS model requires small datasets to train, converges fast, and is executable on ordinary personal computers. Extensive examinations on simulated data and empirical data confirmed that the QFSTS model has superior performance in feature selection, parameter estimation, and forecast.