Modelos estocásticos del esquema de pruebas de resistencia mediante procesos SARIMAX y extensiones con variables exógenas

Abstract

This work is based on the theory of stochastic processes and time series, specifically using concepts such as stationarity, lag operators, differentiating, autoregressive processes, moving average processes, seasonality, exogenous variables, and statistical estimation. In particular, a stochastic modeling methodology is proposed, based on SARIMAX models, to project trajectories under a baseline scenario and an adverse scenario, incorporating exogenous macroeconomic variables. In the applied component, the microcredit, consumer, commercial loan portfolio, and total loan portfolio lines are analyzed. Projected trajectories are constructed for each of these under different scenarios. The results are not presented using absolute values, but rather through percentage variations, relative gaps, and curve interpretation. (This presentation format allows for preserving the quantitative interpretation without revealing sensitive information about the entity.) Among the results, it is observed that the adverse scenario generates lower trajectories compared to the baseline scenario, although sensitivity is not homogeneous across the analyzed lines. It is observed that microcredit presents the greatest relative sensitivity, followed by consumer loans, total portfolio, and commercial portfolio. The SARIMAX model allows for comparing scenarios, measuring sensitivity, and providing a framework for the technical discussion of the EPR (Executive Performance Review). Finally, the model should not be interpreted as a deterministic prediction of the future; rather, it is a prospective tool for evaluating possible trajectories under certain assumptions. Its main contribution lies in linking the rigor of stochastic modeling with a specific need in banking financial analysis within an environment regulated by the Financial Superintendency of Colombia.