Bayesian MIDAS Penalized Regressions: Estimation, Selection, and Prediction

Abstract

We propose a new approach to mixed-frequency regressions in a high-dimensional environment that resorts to Group Lasso penalization and Bayesian techniques for estimation and inference. In particular, to improve the prediction properties of the model and its sparse recovery ability, we consider a Group Lasso with a spike-and-slab prior. Penalty hyper-parameters governing the model shrinkage are automatically tuned via an adaptive MCMC algorithm. We establish good frequentist asymptotic properties of the posterior of the in-sample and out-of-sample prediction error, we recover the optimal posterior contraction rate, and we show optimality of the posterior predictive density.Simulations show that the proposed models have good selection and forecasting performance in small samples, even when the design matrix presents cross-correlation. When applied to forecasting U.S. GDP, our penalized regressions can outperform many strong competitors. Results suggest that financial variables may have some, although very limited, short-term predictive content.

Nowcasting world GDP growth with high‐frequency data

“…Contrary to the FA‐MIDAS, it performs both the selection of regressors and the estimation of the mixed‐frequency equation in a single step. The LASSO‐MIDAS is a recent addition to the literature (Marsilli, 2014; Mogliani & Simoni, 2021; Uematsu & Tanaka, 2019), and the model used in this paper is the sparse‐group LASSO of Babii et al (2021). The interest of the “group‐LASSO” over the unstructured LASSO is that for a given regressor, either all high‐frequency lags enter the regression, or all are set to zero.…”

Gene‐gene interaction analysis incorporating network information via a structured Bayesian approach

“…Specifically, 𝛾 j = 0 leads to the spike component related to s 2 , and 𝛽 j will be truncated to be zero as s 2 has a very small value. Continuous spike and slab priors have been commonly used in practice, because they not only facilitate analysis but also improve the sparse recovery ability of the model 27 and have desirable model selection properties. 28…”

“…26 In addition, they provide a flexible way for estimating other parameters in the model and can provide prediction via predictive distributions. 27 Different from most published Bayesian interaction studies based on the Markov Chain Monte Carlo (MCMC) inference technique, we take advantage of the hybrid model integrating conditional and generative components and develop a more efficient variational Bayesian expectation-maximization algorithm. This is especially desirable with the extremely high dimensions in gene-gene interaction analysis.…”

Nowcasting Unemployment Rates with Smartphone GPS Data

“…A natural extension is a situation where high dimensional (large p) and high frequency predictive variables are present in small sample (smaller N ). Various models combine feature selection techniques and MIDAS are proposed [22][23][24]. Recently Uematsu and Tanaka [25] showed a simple penalized regression without MIDAS technique performs well for GDP forecasting with high frequent data.…”