Mikael Jagan:
Midpoint-Radius Interval Arithmetic and R Package ‘flint’, an R Interface to the FLINT C Library

Interval arithmetic enables computation with automatic propagation of input error.  Defining interval arithmetic in arbitrary but finite precision (hence over a set of floating-point real numbers) raises interesting questions about how to represent intervals in memory and how to implement mathematical functions in light of tradeoffs between optimality of output and efficiency.  In the first half, I survey some of these issues, maintaining a focus on midpoint-radius interval arithmetic, also known as ball arithmetic, and its implementation in the Arb module of the FLINT C library. In the second half, I introduce R package 'flint', an R interface to FLINT, covering design principles, scope, usage, and future development.

Ivan Krylov:
Tensor Decompositions of Fluorescence Spectra: A Case Study in R

Excitation-emission fluorescence spectroscopy is a cheap and sensitive analysis method, which ensures its wide popularity in environmental monitoring. The structure of the resulting data makes it very amenable to tensor decompositions, specifically, PARAFAC, but the process involves a lot of important details. We will explore some of them, including data pre-treatment (surface interpolation), model validation (split-half), implementation and packaging in R (and some auxiliary packages), and take a look at problems still in need of a satisfactory solution, such as regularisation and expansions of the model.

Bezirgen Veliyev:
Realized Principal Component Analysis of Noisy High-Frequency Data

In this paper, we propose a pre-averaging extension of Ait-Sahalia and Xiu (2019), who develop a realized principal component analysis for a continuous-time multi-dimensional log-price process observed discretely over a fixed time interval with vanishing mesh. It applies to study the eigenvalue problem for a time-varying covariance matrix when the high-frequency data are perturbed by measurement error. We derive a consistent noise-robust estimator of the spot covariance in a general framework. Then, exploiting the theory of volatility functional estimation of Jacod and Rosenbaum (2013), we design realized estimators of the integrated eigenvalue, eigenvector and principal component for this setting. We develop a fully-fledged mixed normal distribution theory for the eigenvalue estimator. It presents an asymptotic second-order bias that we show how to correct. In a Monte Carlo study, we document the accuracy of the realized eigenvalue within a standard linear factor model for asset pricing, while an empirical application illuminates its properties on stock market high-frequency data.

Co-authored with Francesco Benvenuti and Kim Christensen.

Antonio Peruzzi:
Media Bias and Polarization Through the Lens of a Markov Switching Latent Space Network Model

News outlets are now more than ever incentivized to provide their audience with slanted news, while the intrinsic homophilic nature of online social media may exacerbate polarized opinions. Here, we propose a new dynamic latent space model for time-varying online audience-duplication networks, which exploits social media content to conduct inference on media bias and polarization of news outlets. We contribute to the literature in several directions: 1) Our model provides a novel measure of media bias that combines information from both network data and text-based indicators; 2) we endow our model with Markov-Switching dynamics to capture polarization regimes while maintaining a parsimonious specification; 3) we contribute to the literature on the statistical properties of latent space network models. The proposed model is applied to a set of data on the online activity of national and local news outlets from four European countries in the years 2015 and 2016. We find evidence of a strong positive correlation between our media slant measure and a well-grounded external source of media bias. In addition, we provide insight into the polarization regimes across the four countries considered.