Dynamic Variable Selection with Spike-and-Slab Process Priors

TL;DR

This paper introduces Dynamic Spike-and-Slab priors for time series regression, enabling effective variable selection that adapts over time, especially in the presence of unknown residual variances, with scalable algorithms demonstrated on macroeconomic data.

Contribution

The paper presents a novel dynamic spike-and-slab prior framework with efficient algorithms for large-scale time series variable selection and uncertainty modeling.

Findings

DSS priors effectively distinguish active from noisy coefficients.

The proposed algorithms perform well on macroeconomic datasets.

The method scales efficiently to large time series data.

Abstract

We address the problem of dynamic variable selection in time series regression with unknown residual variances, where the set of active predictors is allowed to evolve over time. To capture time-varying variable selection uncertainty, we introduce new dynamic shrinkage priors for the time series of regression coefficients. These priors are characterized by two main ingredients: smooth parameter evolutions and intermittent zeroes for modeling predictive breaks. More formally, our proposed Dynamic Spike-and-Slab (DSS) priors are constructed as mixtures of two processes: a spike process for the irrelevant coefficients and a slab autoregressive process for the active coefficients. The mixing weights are themselves time-varying and depend on lagged values of the series. Our DSS priors are probabilistically coherent in the sense that their stationary distribution is fully known and characterized by spike-and-slab marginals. For posterior sampling over dynamic regression coefficients, model selection indicators as well as unknown dynamic residual variances, we propose a Dynamic SSVS algorithm based on forward-filtering and backward-sampling. To scale our method to large data sets, we develop a Dynamic EMVS algorithm for MAP smoothing. We demonstrate, through simulation and a topical macroeconomic dataset, that DSS priors are very effective at separating active and noisy coefficients. Our fast implementation significantly extends the reach of spike-and-slab methods to large time series data.