Monofractal analysis offers a promising framework for characterizing cardiac dynamics, particularly in the early detection of heart failure. However, most existing approaches rely on long-duration physiological signals and do not explore the classification of disease severity. In this study, we propose a hybrid CNN-ELM model trained exclusively on synthetic monofractal time series of short length (128 to 512 samples), aiming to assess its ability to distinguish between healthy individuals and varying degrees of heart failure defined by the NYHA functional classification. Our results show that Hurst exponent distributions reflect the progressive loss of complexity in cardiac rhythms as heart failure severity increases. The model successfully classified both binary (healthy vs. sick) and multiclass (NYHA I–IV) scenarios by grouping Hurst exponent values ($H_{0.1}$ to $H_{0.9}$) into clinical categories, achieving peak accuracy ranges of 97.3–98.9% for binary classification and 96.2–98.8% for multiclass classification across signal lengths of 128, 256, and 512 samples. Importantly, the CNN-ELM architecture demonstrated fast training times and robust generalization, outperforming previous approaches based solely on support vector machines. These findings highlight the clinical potential of monofractal indices as non-invasive biomarkers of cardiovascular health and support the use of short synthetic signals for scalable, low-cost screening applications. Future work will extend this framework to multifractal and real-world clinical data and explore its integration into intelligent diagnostic systems.

Short time series are fundamental in the foreign exchange market due to their ability to provide real-time information, allowing traders to react quickly to market movements, thus optimizing profits and mitigating risks. Economic transactions show a strong connection to foreign currencies, making exchange rate prediction challenging. In this study, the exchange rate estimation between the US dollar (USD) and the Chilean peso (CLP) for a short period, from 2 August 2021 to 31 August 2022, is modeled using the nonlinear Schrödinger equation (NLSE) and calculated with the fourth-order Runge–Kutta method, respectively. Additionally, the daily fluctuations of the current exchange rate are characterized using the Hurst exponent, H, and later used to generate short synthetic fluctuations to predict the USD–CLP exchange rate. The results show that the USD–CLP exchange rate can be estimated with an error of less than $5\%$, while when using short synthetic fluctuations, the exchange rate shows an error of less than $10\%$.