arXiv subjects

Matteo Farnè

Publications and source records attributed to Matteo Farnè.

8 recordsLinked to original sources

arXiv2026

Geometric Regime--Switching Diffusions on Stratified Riemannian Spaces with an Application to Covariance Matrices

We construct geometric regime-switching diffusions, a class of Markov processes on locally compact stratified Riemannian state spaces. In contrast with classical regime-switching and stochastic hybrid diffusions, the regimes are not external labels, but intrinsic strata of a singular geometric state space. Changes of regime may therefore change dimension, rank, geometry or combinatorial type while the state space maintains its ambient topology. On each stratum the motion is a conservative Feller diffusion, while inter-stratum transitions are specified by state-dependent jump rates and landing kernels along a directed graph. We characterize the process through a martingale problem on a natural stratified core. Under a uniform bound on the total jump rate, we construct a conservative c\`adl\`ag strong Markov process by combining the stratumwise diffusions with a Poisson thinning mechanism. Uniqueness is proved using an auxiliary disjoint-union topology and a bounded perturbation argument. Standard Foster--Lyapunov conditions for the extended generator give positive Harris recurrence, uniqueness of the invariant probability measure and, under aperiodicity, $V$-uniform geometric ergodicity. The framework is applied to the cone of positive semidefinite covariance matrices, stratified by rank. The resulting process combines fixed-rank covariance diffusions with stochastic rank changes and is $V$-uniformly geometrically ergodic.

math.PR↗

arXiv2025

The Impact of Climatic Factors on Respiratory Pharmaceutical Demand: A Comparison of Forecasting Models for Greece

Climate change is increasingly recognized as a driver of health-related outcomes, yet its impact on pharmaceutical demand remains largely understudied. As environmental conditions evolve and extreme weather events intensify, anticipating their influence on medical needs is essential for designing resilient healthcare systems. This study examines the relationship between climate variability and the weekly demand for respiratory prescription pharmaceuticals in Greece, based on a dataset spanning seven and a half years (390 weeks). Granger causality spectra are employed to explore potential causal relationships. Following variable selection, four forecasting models are implemented: Prophet, a Vector Autoregressive model with exogenous variables (VARX), Random Forest with Moving Block Bootstrap (MBB-RF), and Long Short-Term Memory (LSTM) networks. The MBB-RF model achieves the best performance in relative error metrics while providing robust insights through variable importance rankings. The LSTM model outperforms most metrics, highlighting its ability to capture nonlinear dependencies. The VARX model, which includes Prophet-based exogenous inputs, balances interpretability and accuracy, although it is slightly less competitive in overall predictive performance. These findings underscore the added value of climate-sensitive variables in modeling pharmaceutical demand and provide a data-driven foundation for adaptive strategies in healthcare planning under changing environmental conditions.

stat.AP↗

arXiv2025

Large covariance matrix estimation via penalized log-det heuristics

This paper provides a comprehensive estimation framework for large covariance matrices via a log-det heuristics augmented by a nuclear norm plus $\ell_{1}$-norm penalty. We develop the model framework, which includes high-dimensional approximate factor models with a sparse residual covariance. We prove that the aforementioned log-det heuristics is locally convex with a Lipschitz-continuous gradient, so that a proximal gradient algorithm may be stated to numerically solve the problem while controlling the threshold parameters. The proposed optimization strategy recovers in a single step both the covariance matrix components and the latent rank and the residual sparsity pattern with high probability, and performs systematically not worse than the corresponding estimators employing Frobenius loss in place of the log-det heuristics. The error bounds for the ensuing low rank and sparse covariance matrix estimators are established, and the identifiability conditions for the latent geometric manifolds are provided, improving existing literature. The validity of outlined results is highlighted by an exhaustive simulation study and a financial data example involving Euro Area banks.

math.ST↗

arXiv2021

Robust selection of predictors and conditional outlier detection in a perturbed large-dimensional regression context

This paper presents a fast methodology, called ROBOUT, to identify outliers in a response variable conditional on a set of linearly related predictors, retrieved from a large granular dataset. ROBOUT is shown to be effective and particularly versatile compared to existing methods in the presence of a number of data idiosyncratic features. ROBOUT is able to identify observations with outlying conditional variance when the dataset contains element-wise sparse variables, and the set of predictors contains multivariate outliers. Existing integrated methodologies like SPARSE-LTS and RLARS are systematically sub-optimal under those conditions. ROBOUT entails a robust selection stage of the statistically relevant predictors (by using a Huber or a quantile loss), the estimation of a robust regression model based on the selected predictors (by LTS, GS or MM), and a criterion to identify conditional outliers based on a robust measure of the residuals' dispersion. We conduct a comprehensive simulation study in which the different variants of the proposed algorithm are tested under an exhaustive set of different perturbation scenarios. The methodology is also applied to a granular supervisory banking dataset collected by the European Central Bank.

stat.ME↗

arXiv2021

Large factor model estimation by nuclear norm plus $l_1$ norm penalization

This paper provides a comprehensive estimation framework via nuclear norm plus $l_1$ norm penalization for high-dimensional approximate factor models with a sparse residual covariance. The underlying assumptions allow for non-pervasive latent eigenvalues and a prominent residual covariance pattern. In that context, existing approaches based on principal components may lead to misestimate the latent rank, due to the numerical instability of sample eigenvalues. On the contrary, the proposed optimization problem retrieves the latent covariance structure and exactly recovers the latent rank and the residual sparsity pattern. Conditioning on them, the asymptotic rates of the subsequent ordinary least squares estimates of loadings and factor scores are provided, the recovered latent eigenvalues are shown to be maximally concentrated and the estimates of factor scores via Bartlett's and Thompson's methods are proved to be the most precise given the data. The validity of outlined results is highlighted in an exhaustive simulation study and in a real financial data example.

math.ST↗

arXiv2021

An algebraic estimator for large spectral density matrices

We propose a new estimator of high-dimensional spectral density matrices, called UNshrunk ALgebraic Spectral Estimator (UNALSE), under the assumption of an underlying low rank plus sparse structure, as typically assumed in dynamic factor models. The UNALSE is computed by minimizing a quadratic loss under a nuclear norm plus $l_1$ norm constraint to control the latent rank and the residual sparsity pattern. The loss function requires as input the classical smoothed periodogram estimator and two threshold parameters, the choice of which is thoroughly discussed. We prove consistency of UNALSE as both the dimension $p$ and the sample size $T$ diverge to infinity, as well as algebraic consistency, i.e., the recovery of latent rank and residual sparsity pattern with probability one. The finite sample properties of UNALSE are studied by means of an extended simulation exercise as well as an empirical analysis of US macroeconomic data.

math.ST↗

arXiv2019

European banks' business models and their credit risk: A cluster analysis in a high-dimensional context

In this paper, we investigate the credit risk in the loan portfolio of banks following different business models. We develop a data-driven methodology for identifying the business models of the 365 largest European banks that is suitable for very granular harmonised supervisory data. Our dataset allows us to take into account the full range of the activities in which banks are involved. The proposed method combines in an optimal way data clustering, dimensionality reduction and outlier detection. We identify four business models and exclude as 'outliers' banks that follow idiosyncratic business models. Furthermore, empirical evidence is provided that banks following different business models differ significantly with respect to the credit risk they undertake in their loan portfolios. Traditional commercial banks are characterized by the lowest levels of credit risk while the loan portfolios of securities holding banks are riskier compared to the other banks.

stat.AP↗

arXiv2018

A large covariance matrix estimator under intermediate spikiness regimes

The present paper concerns large covariance matrix estimation via composite minimization under the assumption of low rank plus sparse structure. In this approach, the low rank plus sparse decomposition of the covariance matrix is recovered by least squares minimization under nuclear norm plus $l_1$ norm penalization. This paper proposes a new estimator of that family based on an additional least-squares re-optimization step aimed at un-shrinking the eigenvalues of the low rank component estimated at the first step. We prove that such un-shrinkage causes the final estimate to approach the target as closely as possible in Frobenius norm while recovering exactly the underlying low rank and sparsity pattern. Consistency is guaranteed when $n$ is at least $O(p^{\frac{3}{2}δ})$, provided that the maximum number of non-zeros per row in the sparse component is $O(p^δ)$ with $δ\leq \frac{1}{2}$. Consistent recovery is ensured if the latent eigenvalues scale to $p^α$, $α\in[0,1]$, while rank consistency is ensured if $δ\leq α$. The resulting estimator is called UNALCE (UNshrunk ALgebraic Covariance Estimator) and is shown to outperform state of the art estimators, especially for what concerns fitting properties and sparsity pattern detection. The effectiveness of UNALCE is highlighted on a real example regarding ECB banking supervisory data.

stat.ME↗