Too big to fail? An analysis of the Colombian banking system through compositional data

Although still incipient in economics and finance, compositional data analysis (in which relative information is more important than absolute values) has become more relevant in statistical analysis in recent years. This article constructs a concentration index for financial/banking systems by means of compositional analysis, to establish the potential existence of too big to fail financial entities. The intention is to provide an early warning tool for regulators about this kind of institutions. The index has been applied to the Colombian banking system and assessed over time with a forecast to determine whether the system is becoming more concentrated or not. It was found that the concentration index has been decreasing in recent years and the model predicts that this trend will continue. In terms of the methodology used, compositional models were shown to be more stable and to lead to better prediction of the index than the classical multivariate methodologies

Sequential Change-point Detection for Compositional Time Series with Exogenous Variables

Sequential change-point detection for time series enables us to sequentially check the hypothesis that the model still holds as more and more data are observed. It is widely used in data monitoring in practice. In this work, we consider sequential change-point detection for compositional time series, time series in which the observations are proportions. For fitting compositional time series, we propose a generalized Beta AR(1) model, which can incorporate exogenous variables upon which the time series observations are dependent. We show the compositional time series are strictly stationary and geometrically ergodic and consider maximum likelihood estimation for model parameters. We show the partial MLEs are consistent and asymptotically normal and propose a parametric sequential change-point detection method for the compositional time series model. The change-point detection method is illustrated using a time series of Covid-19 positivity rates