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 Schr & ouml;dinger 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%.