The usefulness of Bayesian models for density and cluster estimation is well established across multiple literatures. However, there is still a known tension between the use of simpler, more interpretable models and more flexible, complex ones. In this paper, we propose a novel method that integrates these two approaches by projecting the fit of a flexible, overparameterized model onto a lower-dimensional parametric surrogate, which serves as a summary. This process increases interpretability while preserving most of the fit of the original model. Our approach involves three main steps. First, we fit the data using nonparametric or overparameterized models. Second, we project the posterior predictive distribution of the original model onto a sequence of parametric summary point estimates with varying dimensions using a decision-theoretic approach. Finally, given the parametric summary estimate, obtained in the second step, that best approximates the original model, we construct uncertainty quantification for this summary by projecting the original posterior distribution. We demonstrate the effectiveness of our method for generating summaries for both nonparametric and overparameterized models, delivering both point estimates and uncertainty quantification for density and cluster summaries across synthetic and real datasets.

In this article, we present a dynamic version of the integer autoregressive (INAR) processes for count data. The proposed Bayesian model provides a unification of the previously considered models to describe temporal correlations in univariate time series of counts. We develop Bayesian inference for the proposed class of models via MCMC and introduce a particle filtering (PF) algorithm for sequential inference. The new class of models are compared with their static counterparts using actual count series and additional insights provided by the new models are discussed.

There has been increased research interest in the subfield of sparse Bayesian factor analysis with shrinkage priors, which achieve additional sparsity beyond the natural parsimonity of factor models. In this spirit, we estimate the number of common factors in the highly implemented sparse latent factor model with spike-and-slab priors on the factor loadings matrix. Our framework leads to a natural, efficient and simultaneous coupling of model estimation and selection on one hand and model identification and rank estimation (number of factors) on the other hand. More precisely, by embedding the unordered generalized lower triangular loadings representation into overfitting sparse factor modelling, we obtain posterior summaries regarding factor loadings, common factors as well as the factor dimension via postprocessing draws from our efficient and customized Markov chain Monte Carlo scheme.

In the present work, we consider variable selection and shrinkage for the Gaussian dynamic linear regression within a Bayesian framework. In particular, we propose a novel method that allows for time-varying sparsity, based on an extension of spike-and-slab priors for dynamic models. This is done by assigning appropriate Markov switching priors for the time-varying coefficients' variances, extending the previous work of Ishwaran and Rao (2005). Furthermore, we investigate different priors, including the common Inverted gamma prior for the process variances, and other mixture prior distributions such as Gamma priors for both the spike and the slab, which leads to a mixture of Normal-Gammas priors (Griffin ad Brown, 2010) for the coefficients. In this sense, our prior can be view as a dynamic variable selection prior which induces either smoothness (through the slab) or shrinkage towards zero (through the spike) at each time point. The MCMC method used for posterior computation uses Markov latent variables that can assume binary regimes at each time point to generate the coefficients' variances. In that way, our model is a dynamic mixture model, thus, we could use the algorithm of Gerlach et al (2000) to generate the latent processes without conditioning on the states. Finally, our approach is exemplified through simulated examples and a real data application.

This article investigates the benefits of combining information available from daily and intraday data in financial return forecasting. The two data sources are combined via a density pooling approach, wherein the individual densities are represented as a copula function, and the potentially time-varying pooling weights depend on the forecasting performance of each model. The dependence structure in the daily frequency case is extracted from a standard static and dynamic conditional covariance modeling, and the high-frequency counterpart is based on a realized covariance measure. We find that incorporating both high- and low-frequency information via density pooling provides significant gains in predictive model performance over any individual model and any model combination within the same data frequency. A portfolio allocation exercise quantifies the economic gains by producing investment portfolios with the smallest variance and highest Sharpe ratio. (c) 2024 The Authors. Published by Elsevier B.V. on behalf of International Institute of Forecasters. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

This paper develops a performant Bayesian approach to conditional average treatment effect (CATE) estimation in regression discontinuity designs (RDD), an increasingly prevalent form of quasi-experiment that facilitates causal inference. Earlier Bayesian approaches do not easily accommodate CATE estimation while recent frequentist approaches to this problem assume a known basis expansion, a steep model specification requirement that our approach avoids. The new model is a variant of a Bayesian additive regression tree (BART) model with linear leaf-level regressions on the running variable and a treatment dummy (and their interaction). The model adaptively partitions covariate space into regions where the slope on the running variable appreciably differs, providing interpretable Bayesian inference on conditional average treatment effects near the cutoff.

In many fields where the main goal is to produce sequential forecasts for decision making problems, the good understanding of the contemporaneous relations among different series is crucial for the estimation of the covariance matrix. In recent years, the modified Cholesky decomposition appeared as a popular approach to covariance matrix estimation. However, its main drawback relies on the imposition of the series ordering structure. In this work, we propose a highly flexible and fast method to deal with the problem of ordering uncertainty in a dynamic fashion with the use of Dynamic Order Probabilities. We apply the proposed method in two different forecasting contexts. The first is a dynamic portfolio allocation problem, where the investor is able to learn the contemporaneous relationships among different currencies improving final decisions and economic performance. The second is a macroeconomic application, where the econometrician can adapt sequentially to new economic environments, switching the contemporaneous relations among macroeconomic variables over time.

This paper introduces BART-RDD, a sum-of-trees regression model built around a novel regression tree prior, which incorporates the special covariate structure of regression discontinuity designs. Specifically, the tree splitting process is constrained to ensure overlap within a narrow band surrounding the running variable cutoff value, where the treatment effect is identified. It is shown that unmodified BART-based models estimate RDD treatment effects poorly, while our modified model accurately recovers treatment effects at the cutoff. Specifically, BART-RDD is perhaps the first RDD method that effectively learns conditional average treatment effects. The new method is investigated in thorough simulation studies as well as an empirical application looking at the effect of academic probation on student performance in subsequent terms (Lindo et al., 2010).

This paper expands traditional stochastic volatility models by allowing for time-varying skewness without imposing it. While dynamic asymmetry may capture the likely direction of future asset returns, it comes at the risk of leading to overparameterization. Our proposed approach mitigates this concern by leveraging sparsity-inducing priors to automatically select the skewness parameter as dynamic, static or zero in a data-driven framework. We consider two empirical applications. First, in a bond yield application, dynamic skewness captures interest rate cycles of monetary easing and tightening and is partially explained by central banks’ mandates. In a currency modeling framework, our model indicates no skewness in the carry factor after accounting for stochastic volatility. This supports the idea of carry crashes resulting from volatility surges instead of dynamic skewness.

Factor Analysis is a popular method for modeling dependence in multivariate data. However, determining the number of factors and obtaining a sparse orientation of the loadings are still major challenges. In this paper, we propose a decision-theoretic approach that brings to light the relation between a sparse representation of the loadings and factor dimension. This relation is done through a summary from information contained in the multivariate posterior. To construct such summary, we introduce a three-step approach. In the first step, the model is fitted with a conservative factor dimension. In the second step, a series of sparse point-estimates, with a decreasing number of factors, is obtained by minimizing an expected predictive loss function. In step three, the degradation in utility in relation to the sparse loadings and factor dimensions is displayed in the posterior summary. The findings are illustrated with applications in classical data from the Factor Analysis literature. We used different prior choices and factor dimensions to demonstrate the flexibility of the proposed method.

We propose a hybrid deep learning model that merges Variational Autoencoders and Convolutional LSTM Networks (VAE-ConvLSTM) to forecast inflation. Using a public macroeconomic database that comprises 134 monthly US time series from January 1978 to December 2019, the proposed model is compared against several popular econometric and machine learning benchmarks, including Ridge regression, LASSO regression, Random Forests, Bayesian methods, VECM, and multilayer perceptron. We find that VAE-ConvLSTM outperforms the competing models in terms of consistency and out-of-sample performance. The robustness of such conclusion is ensured via cross-validation and Monte-Carlo simulations using different training, validation, and test samples. Our results suggest that macroeconomic forecasting could take advantage of deep learning models when tackling nonlinearities and nonstationarity, potentially delivering superior performance in comparison to traditional econometric approaches based on linear, stationary models.

Analysis of the currently established Bayesian nearest neighbors classification model points to a connection between the computation of its normalizing constant and issues of NP-completeness. An alternative predictive model constructed by aggregating the predictive distributions of simpler nonlocal models is proposed, and analytic expressions for the normalizing constants of these nonlocal models are derived, ensuring polynomial time computation without approximations. Experiments with synthetic and real datasets showcase the predictive performance of the proposed predictive model.

Despite the popularity of factor models with simple loading matrices, little attention has been given to formally address the identifiability of these models beyond standard rotation-based identification such as the positive lower triangular (PLT) constraint. To fill this gap, we review the advantages of variance identification in simple factor analysis and introduce the generalized lower triangular (GLT) structures. We show that the GLT assumption is an improvement over PLT without compromise: GLT is also unique but, unlike PLT, a non-restrictive assumption. Furthermore, we provide a simple counting rule for variance identification under GLT structures, and we demonstrate that within this model class, the unknown number of common factors can be recovered in an exploratory factor analysis. Our methodology is illustrated for simulated data in the context of post-processing posterior draws in sparse Bayesian factor analysis.

State–space models are commonly used in the engineering, economic, and statistical literature. They are flexible and encompass many well-known statistical models, including random coefficient autoregressive models and dynamic factor models. Bayesian analysis of state–space models has attracted much interest in recent years. However, for large scale models, prior specification becomes a challenging issue in Bayesian inference. In this paper, we propose a flexible prior for state–space models. The proposed prior is a mixture of four commonly entertained models, yet achieving parsimony in high-dimensional systems. Here “parsimony” is represented by the idea that, in a large system, some states may not be time-varying. Our prior for the state–space component’s standard deviation is capable to accommodate different scenarios. Simulation and simple examples are used throughout this paper to demonstrate the performance of the proposed prior. As an application, we consider the time-varying conditional covariance matrices of daily log returns of the components of the S&P 100 index, leading to a state–space model with roughly five thousand time-varying states. Our model for this large system enables us to use parallel computing.

The emergence of Big Data raises the question of how to model economic relations when there is a large number of possible explanatory variables. We revisit the issue by comparing the possibility of using dense or sparse models in a Bayesian approach, allowing for variable selection and shrinkage. More specifically, we discuss the results reached by Giannone, Lenza, and Primiceri (2020) through a "Spike-and-Slab" prior, which suggest an "illusion of sparsity" in economic data, as no clear patterns of sparsity could be detected. We make a further revision of the posterior distributions of the model, and propose three experiments to evaluate the robustness of the adopted prior distribution. We find that the pattern of sparsity is sensitive to the prior distribution of the regression coefficients, and present evidence that the model indirectly induces variable selection and shrinkage, which suggests that the "illusion of sparsity" could be, itself, an illusion. Code is available on github.com/bfava/IllusionOfIllusion.

We propose a fast and flexible method to scale multivariate return volatility predictions up to high-dimensions using a dynamic risk factor model. Our approach increases parsimony via time-varying sparsity on factor loadings and is able to sequentially learn the use of constant or time-varying parameters and volatilities. We show in a dynamic portfolio allocation problem with 452 stocks from the S&P 500 index that our dynamic risk factor model is able to produce more stable and sparse predictions, achieving not just considerable portfolio performance improvements but also higher utility gains for the mean-variance investor compared to the traditional Wishart benchmark and the passive investment on the market index.

The high hospitalization rate of patients with coronavirus disease (COVID-19) has led to the collapse of healthcare systems in many countries. Vaccines for COVID-19 emerged in late 2020, and they have been shown to be a powerful tool to decrease hospitalization numbers in countries that were able to quickly vaccinate a majority of their populations (). The goal of this study was to estimate how many COVID-19-related hospitalizations were prevented in the state of Sao Paulo (Brazil) because of vaccines [...]

Time series momentum strategies are widely applied in the quantitative financial industry and its academic research has grown rapidly since the work of Moskowitz, Ooi and Pedersen (2012). However, trading signals are usually obtained via simple observation of past return measurements. In this article we study the benefits of incorporating dynamic econometric models to sequentially learn the time-varying importance of different look-back periods for individual assets. By the use of a dynamic binary classifier model, the investor is able to switch between time-varying or constant relations between past momentum and future returns, dynamically combining or selecting different momentum speeds during turning points, improving trading signals accuracy and portfolio performance. Using data from 56 future contracts we show that a mean-variance investor will be willing to pay a considerable management fee to switch from the traditional naive time series momentum strategy to the dynamic classifier approach.

We examine issues of prior sensitivity in a semi-parametric hierarchical extension of the INAR(p) model with innovation rates clustered according to a Pitman–Yor process placed at the top of the model hierarchy. Our main finding is a graphical criterion that guides the specification of the hyperparameters of the Pitman–Yor process base measure. We show how the discount and concentration parameters interact with the chosen base measure to yield a gain in terms of the robustness of the inferential results. The forecasting performance of the model is exemplified in the analysis of a time series of worldwide earthquake events, for which the new model outperforms the original INAR(p) model.

One of the major concerns engendered by a warming climate are changing sea levels and their lasting effects on coastal populations, infrastructures, and natural habitats. Sea levels are now monitored by satellites, but long‐term records are only available at discrete locations along the coasts. Sea levels and sea‐level processes must be better understood at the local level to best inform real‐world adaptation decisions. We propose a statistical model that facilitates the characterization of known sea‐level processes, which jointly govern the observed sea level along the United States Atlantic Coast. Our model not only incorporates long‐term sea level rise and seasonal cycles but also accurately accounts for residual spatiotemporal processes. By combining a spatially varying coefficient modeling approach with spatiotemporal factor analysis methods in a Bayesian framework, the method represents the contribution of each of these processes and accounts for corresponding dependencies and uncertainties in a coherent way. Additionally, the model provides a consistent way to estimate these processes and sea level values at unmonitored locations along the coast. We show the outcome of the proposed model using thirty years of sea level data from 38 stations along the Atlantic (east) Coast of the United States. Among other results, our method estimates the rate of sea level rise to range from roughly 1 mm/year in the northern and southern regions of the Atlantic coast to 5.4 mm/year in the middle region.