arXiv subjects

Mauro Bernardi

Publications and source records attributed to Mauro Bernardi.

At least 19 recordsLinked to original sources

arXiv2026

Flexible variational approximations for stochastic volatility-managed portfolios

This paper investigates volatility-managed portfolios through a variational Bayes approach that smooths stochastic volatility forecasts. Our algorithm exhibits competitive performance relative to established methods both in terms of inferential accuracy and computational efficiency. Analyzing equity factors and characteristic-based portfolios, we show that smoothing reduces excess leverage and turnover, significantly improving risk-adjusted returns after transaction costs. Importantly, our smoothed stochastic volatility method achieves positive net performance while avoiding extreme negative outcomes, a combination no competing approach attains. We demonstrate that superior forecasting accuracy does not guarantee superior portfolio performance, revealing a fundamental trade-off between model precision and economic utility.

econ.EM↗

arXiv2026

Degrees of Freedom in Penalized Regression: Model Selection with Adaptive Penalties

Model selection in penalized regression critically depends on an accurate assessment of model complexity, commonly quantified through the effective degrees of freedom. While the Lasso admits a simple and unbiased characterization, given by the size of the active set, this property does not extend to adaptive penalization methods, despite the widespread use of this approximation in practice. To solve this issue, in this paper we derive a novel unbiased estimator of the effective degrees of freedom for the Adaptive Lasso within Stein's unbiased risk estimation framework. Our analysis reveals additional terms induced by data-dependent penalization, reflecting the role of adaptive weights and regularization in determining model complexity. We further revisit the Group Lasso, providing an alternative derivation of its degrees of freedom, and extend these results to the Adaptive Group Lasso. Importantly, we characterize the behavior of the degrees of freedom along the regularization path beyond the orthonormal design setting commonly assumed in the literature, providing a new theoretical description of this behavior under general design matrices. By correcting the common misuse of active set size as a proxy for degrees of freedom, our results enable more reliable risk estimation and inference, offering a rigorous foundation for understanding model complexity in adaptive penalized regression.

stat.ME↗

arXiv2026

Fast QR updating methods for statistical applications

This paper introduces fast R updating algorithms specifically designed for statistical applications, including regression, filtering, and model selection, where data structures change frequently. Although traditional QR decomposition is essential for matrix operations, it becomes computationally intensive when dynamically updating the design matrix in statistical models. The proposed algorithms efficiently update the R matrix without the need for recalculation of Q, thereby significantly reducing computational costs in practical computational scenarios. The provision of scalable solutions for high-dimensional regression models is a key strength of these algorithms, enhancing the feasibility of large-scale statistical analyses and model selection in data-intensive fields. A thorough simulation study and the analysis of real-world data demonstrate that the methods achieve a substantial reduction in computational time without compromising accuracy. The discussion illustrates the benefits of these algorithms across a wide range of models and applications in statistics and machine learning.

stat.ME↗

arXiv2025

Non-conjugate variational Bayes for pseudo-likelihood mixed effect models

We propose a unified, yet simple to code, non-conjugate variational Bayes algorithm for posterior approximation of generic Bayesian generalized mixed effect models. Specifically, we consider regression models identified by a linear predictor, eventually transformed using a bijective link, where the prediction misfit is measured using, possibly non-differentiable, loss functions. Examples include generalized linear models, quasi-likelihood models, and robust regression. To address the limitations of non-conjugate settings, we employ an efficient message passing optimization strategy under a Gaussian variational approximation of the posterior. The resulting algorithms automatically account for non-conjugate priors and non-smooth losses, without requiring model-specific data-augmented representations. Besides the general formulation, we provide closed-form updates for popular model specifications, including quantile regression and support vector machines. Overall, theoretical and empirical results highlight the effectiveness of the proposed method, demonstrating its computational efficiency and approximation accuracy as an alternative to existing Bayesian techniques.

stat.ME↗

arXiv2025

Scalable Variational Bayes Inference for Dynamic Variable Selection

We develop a variational Bayes approach for dynamic variable selection in high-dimensional regression models with time-varying parameters and predictors that exhibit a predefined group structure. Through comprehensive simulation studies, we demonstrate that our method yields more accurate parameter estimates than existing Bayesian static and dynamic variable selection approaches while maintaining computational efficiency. We illustrate the performance of our approach within the context of a popular problem in economics: forecasting inflation based on a large set of macroeconomic predictors. Our approach demonstrates significant improvements in out-of-sample point and density forecasting accuracy. A retrospective analysis of the time-varying parameter estimates reveals economically interpretable patterns in inflation dynamics.

stat.ME↗

arXiv2024

Bayesian Dynamic Quantile Model Averaging

This article introduces a novel dynamic framework to Bayesian model averaging for time-varying parameter quantile regressions. By employing sequential Markov chain Monte Carlo, we combine empirical estimates derived from dynamically chosen quantile regressions, thereby facilitating a comprehensive understanding of the quantile model instabilities. The effectiveness of our methodology is initially validated through the examination of simulated datasets and, subsequently, by two applications to the US inflation rates and to the US real estate market. Our empirical findings suggest that a more intricate and nuanced analysis is needed when examining different sub-period regimes, since the determinants of inflation and real estate prices are clearly shown to be time-varying. In conclusion, we suggest that our proposed approach could offer valuable insights to aid decision making in a rapidly changing environment.

math.ST↗

arXiv2023

Variational inference for large Bayesian vector autoregressions

We propose a novel variational Bayes approach to estimate high-dimensional vector autoregression (VAR) models with hierarchical shrinkage priors. Our approach does not rely on a conventional structural VAR representation of the parameter space for posterior inference. Instead, we elicit hierarchical shrinkage priors directly on the matrix of regression coefficients so that (1) the prior structure directly maps into posterior inference on the reduced-form transition matrix, and (2) posterior estimates are more robust to variables permutation. An extensive simulation study provides evidence that our approach compares favourably against existing linear and non-linear Markov Chain Monte Carlo and variational Bayes methods. We investigate both the statistical and economic value of the forecasts from our variational inference approach within the context of a mean-variance investor allocating her wealth in a large set of different industry portfolios. The results show that more accurate estimates translate into substantial statistical and economic out-of-sample gains. The results hold across different hierarchical shrinkage priors and model dimensions.

econ.EM↗

arXiv2022

Missing data patterns in runners' careers: do they matter?

Predicting the future performance of young runners is an important research issue in experimental sports science and performance analysis. We analyse a data set with annual seasonal best performances of male middle distance runners for a period of 14 years and provide a modelling framework that accounts for both the fact that each runner has typically run in three distance events (800, 1500 and 5000 meters) and the presence of periods of no running activities. We propose a latent class matrix-variate state space model and we empirically demonstrate that accounting for missing data patterns in runners' careers improves the out of sample prediction of their performances over time. In particular, we demonstrate that for this analysis, the missing data patterns provide valuable information for the prediction of runner's performance.

stat.AP↗

arXiv2022

Doubly-online changepoint detection for monitoring health status during sports activities

We provide an online framework for analyzing data recorded by smart watches during running activities. In particular, we focus on identifying variations in the behavior of one or more measurements caused by changes in physical condition, such as physical discomfort, periods of prolonged de-training, or even the malfunction of measuring devices. Our framework considers data as a sequence of running activities represented by multivariate time series of physical and biometric data. We combine classical changepoint detection models with an unknown number of components with Gaussian state space models to detect distributional changes between a sequence of activities. The model considers multiple sources of dependence due to the sequential nature of subsequent activities, the autocorrelation structure within each activity, and the contemporaneous dependence between different variables. We provide an online Expectation-Maximization (EM) algorithm involving a sequential Monte Carlo (SMC) approximation of changepoint predicted probabilities. As a byproduct of our model assumptions, our proposed approach processes sequences of multivariate time series in a doubly-online framework. While classical changepoint models detect changes between subsequent activities, the state space framework coupled with the online EM algorithm provides the additional benefit of estimating the real-time probability that a current activity is a changepoint.

stat.AP↗

arXiv2021

Locally Sparse Function on function Regression

In functional data analysis, functional linear regression has attracted significant attention recently. Herein, we consider the case where both the response and covariates are functions. There are two available approaches for addressing such a situation: concurrent and nonconcurrent functional models. In the former, the value of the functional response at a given domain point depends only on the value of the functional regressors evaluated at the same domain point, whereas, in the latter, the functional covariates evaluated at each point of their domain have a non-null effect on the response at any point of its domain. To balance these two extremes, we propose a locally sparse functional regression model in which the functional regression coefficient is allowed (but not forced) to be exactly zero for a subset of its domain. This is achieved using a suitable basis representation of the functional regression coefficient and exploiting an overlapping group-Lasso penalty for its estimation. We introduce efficient computational strategies based on majorization-minimization algorithms and discuss appealing theoretical properties regarding the model support and consistency of the proposed estimator. We further illustrate the empirical performance of the method through simulations and two applications related to human mortality and bidding the energy market.

stat.ME↗

arXiv2021

Identification of high-energy astrophysical point sources via hierarchical Bayesian nonparametric clustering

The light we receive from distant astrophysical objects carries information about their origins and the physical mechanisms that power them. The study of these signals, however, is complicated by the fact that observations are often a mixture of the light emitted by multiple localized sources situated in a spatially-varying background. A general algorithm to achieve robust and accurate source identification in this case remains an open question in astrophysics. This paper focuses on high-energy light (such as X-rays and gamma-rays), for which observatories can detect individual photons (quanta of light), measuring their incoming direction, arrival time, and energy. Our proposed Bayesian methodology uses both the spatial and energy information to identify point sources, that is, separate them from the spatially-varying background, to estimate their number, and to compute the posterior probabilities that each photon originated from each identified source. This is accomplished via a Dirichlet process mixture while the background is simultaneously reconstructed via a flexible Bayesian nonparametric model based on B-splines. Our proposed method is validated with a suite of simulation studies and illustrated with an application to a complex region of the sky observed by the \emph{Fermi} Gamma-ray Space Telescope.

stat.AP↗

arXiv2019

Unified Bayesian Conditional Autoregressive Risk Measures using the Skew Exponential Power Distribution

Conditional Autoregressive Value-at-Risk and Conditional Autoregressive Expectile have become two popular approaches for direct measurement of market risk. Since their introduction several improvements both in the Bayesian and in the classical framework have been proposed to better account for asymmetry and local non-linearity. Here we propose a unified Bayesian Conditional Autoregressive Risk Measures approach by using the Skew Exponential Power distribution. Further, we extend the proposed models using a semiparametric P-spline approximation answering for a flexible way to consider the presence of non-linearity. To make the statistical inference we adapt the MCMC algorithm proposed in Bernardi et al. (2018) to our case. The effectiveness of the whole approach is demonstrated using real data on daily return of five stock market indices.

q-fin.ST↗

arXiv2017

The Sparse Multivariate Method of Simulated Quantiles

In this paper the method of simulated quantiles (MSQ) of Dominicy and Veredas (2013) and Dominick et al. (2013) is extended to a general multivariate framework (MMSQ) and to provide a sparse estimator of the scale matrix (sparse-MMSQ). The MSQ, like alternative likelihood-free procedures, is based on the minimisation of the distance between appropriate statistics evaluated on the true and synthetic data simulated from the postulated model. Those statistics are functions of the quantiles providing an effective way to deal with distributions that do not admit moments of any order like the $α$-Stable or the Tukey lambda distribution. The lack of a natural ordering represents the major challenge for the extension of the method to the multivariate framework. Here, we rely on the notion of projectional quantile recently introduced by Hallin etal. (2010) and Kong Mizera (2012). We establish consistency and asymptotic normality of the proposed estimator. The smoothly clipped absolute deviation (SCAD) $\ell_1$--penalty of Fan and Li (2001) is then introduced into the MMSQ objective function in order to achieve sparse estimation of the scaling matrix which is the major responsible for the curse of dimensionality problem. We extend the asymptotic theory and we show that the sparse-MMSQ estimator enjoys the oracle properties under mild regularity conditions. The method is illustrated and its effectiveness is tested using several synthetic datasets simulated from the Elliptical Stable distribution (ESD) for which alternative methods are recognised to perform poorly. The method is then applied to build a new network-based systemic risk measurement framework. The proposed methodology to build the network relies on a new systemic risk measure and on a parametric test of statistical dominance.

stat.ME↗

arXiv2016

On the Lp-quantiles for the Student t distribution

L_p-quantiles represent an important class of generalised quantiles and are defined as the minimisers of an expected asymmetric power function, see Chen (1996). For p=1 and p=2 they correspond respectively to the quantiles and the expectiles. In his paper Koenker (1993) showed that the tau quantile and the tau expectile coincide for every tau in (0,1) for a class of rescaled Student t distributions with two degrees of freedom. Here, we extend this result proving that for the Student t distribution with p degrees of freedom, the tau quantile and the tau L_p-quantile coincide for every tau in (0,1) and the same holds for any affine transformation. Furthermore, we investigate the properties of L_p-quantiles and provide recursive equations for the truncated moments of the Student t distribution.

stat.ME↗

arXiv2016

Bayesian Robust Quantile Regression

Traditional Bayesian quantile regression relies on the Asymmetric Laplace distribution (ALD) mainly because of its satisfactory empirical and theoretical performances. However, the ALD displays medium tails and it is not suitable for data characterized by strong deviations from the Gaussian hypothesis. In this paper, we propose an extension of the ALD Bayesian quantile regression framework to account for fat-tails using the Skew Exponential Power (SEP) distribution. Beside having the $τ$-level quantile as parameter, the SEP distribution has an additional key parameter governing the decay of the tails, making it attractive for robust modeling of conditional quantiles at different confidence levels. Linear and Generalized Additive Models (GAM) with penalized spline are considered to show the flexibility of the SEP in the Bayesian quantile regression context. Lasso priors are considered in both cases to account for shrinking parameters problem when the parameters space becomes wide. To implement the Bayesian inference we propose a new adaptive Metropolis--Hastings algorithm in the linear model and an adaptive Metropolis within Gibbs one in the GAM framework. Empirical evidence of the statistical properties of the proposed SEP Bayesian quantile regression method is provided through several example based on simulated and real dataset.

stat.ME↗

arXiv2016

Switching-GAS Copula Models With Application to Systemic Risk

Recent financial disasters have emphasised the need to accurately predict extreme financial losses and their consequences for the institutions belonging to a given financial market. The ability of econometric models to predict extreme events strongly relies on their flexibility to account for the highly nonlinear and asymmetric dependence observed in financial returns. We develop a new class of flexible Copula models where the evolution of the dependence parameters follow a Markov-Switching Generalised Autoregressive Score (SGASC) dynamics. Maximum Likelihood estimation is consistently performed using the Inference Functions for Margins (IFM) approach and a version of the Expectation-Maximisation (EM) algorithm specifically tailored to this class of models. The SGASC models are then used to estimate the Conditional Value-at-Risk (CoVaR), which is defined as the VaR of a given asset conditional on another asset (or portfolio) being in financial distress, and the Conditional Expected Shortfall (CoES). Our empirical investigation shows that the proposed SGASC models are able to explain and predict the systemic risk contribution of several European countries. Moreover, we also find that the SGASC models outperform competitors using several CoVaR backtesting procedures.

stat.ME↗

arXiv2016

Portfolio Optimisation Under Flexible Dynamic Dependence Modelling

Signals coming from multivariate higher order conditional moments as well as the information contained in exogenous covariates, can be effectively exploited by rational investors to allocate their wealth among different risky investment opportunities. This paper proposes a new flexible dynamic copula model being able to explain and forecast the time-varying shape of large dimensional asset returns distributions. Moreover, we let the univariate marginal distributions to be driven by an updating mechanism based on the scaled score of the conditional distribution. This framework allows us to introduce time-variation in up to the fourth moment of the conditional distribution. The time-varying dependence pattern is subsequently modelled as function of a latent Markov Switching process, allowing also for the inclusion of exogenous covariates in the dynamic updating equation. We empirically assess that the proposed model substantially improves the optimal portfolio allocation of rational investors maximising their expected utility.

q-fin.PM↗

arXiv2015

Comparison of Value-at-Risk models: the MCS package

This paper compares the Value--at--Risk (VaR) forecasts delivered by alternative model specifications using the Model Confidence Set (MCS) procedure recently developed by Hansen et al. (2011). The direct VaR estimate provided by the Conditional Autoregressive Value--at--Risk (CAViaR) models of Eengle and Manganelli (2004) are compared to those obtained by the popular Autoregressive Conditional Heteroskedasticity (ARCH) models of Engle (1982) and to the recently introduced Generalised Autoregressive Score (GAS) models of Creal et al. (2013) and Harvey (2013). The Hansen's procedure consists on a sequence of tests which permits to construct a set of "superior" models, where the null hypothesis of Equal Predictive Ability (EPA) is not rejected at a certain confidence level. Our empirical results, suggest that, after the Global Financial Crisis (GFC) of 2007-2008, highly non-linear volatility models deliver better VaR forecasts for the European countries as opposed to other regions. The R package MCS is introduced for performing the model comparisons whose main features are discussed throughout the paper.

stat.CO↗