Dynamic graph in a symbolic data framework: An account of the causal relation using COVID-19 reports and some reflections on the financial world

Abstract

This article aims to evaluate a complex relation structure represented by a graph, considering a high dimensional dataset in the Symbolic Data Analysis domain. We consider COVID-19 pandemic dynamic data regarding the first semester of 2020 associated with the daily infection rate in 214 countries with remarkable trends from the financial market; thus, the empirical causality. This work is innovative as we developed a dynamic graphical model for interval data based on center-range representation, which can shrink the parametric high-dimensional time series space and uncovers causal relations. Symbolic Data Analysis provides tools to reduce data dimension through the fusion of multivariate time series in data classes, which allows considering complex information through symbolic interval multivalued variables. Additionally, the Multiregression Dynamic Model (MDM) approach estimates a Directed Acyclic Graph (DAG) which distinguishes structural changes and irregular patterns by modeling the joint learning of multivariate time series, that is, allowing heterogeneous pattern collections and simultaneously estimating relationships across series, now as symbolic interval data. Time-varying parameter estimates of allowed us to translate the influence (internal and external) of these structures dynamically, during the first months of 2020, on the interconnectedness of global regions and the spread of coronavirus worldwide. Then, descriptions of the internal variation of the regions are obtained, after the first months of the semester, reflecting the lockdown (that is, the virus transmission occurs in a generalized way worldwide, then reduced, but concentrated within the regions and not more between them). Finally, an association was sought on the impact of the disclosure (news) of COVID-19 and empirical impacts with performances of the main indices of the global financial market, in which an association between these phenomena was noticeable.