The aim of this paper is to present the benefits of including the pattern of persistence through the Hurst constant in the forecasting of financial time series. In particular, it is done a forecast of the benchmark series of market prices with larger trading volumes in Colombia, the daily interest rates of zero coupon bonds generated by the Central Bank. For this, it is use the information in a time frame 2003 to 2015 to get the results and compare the processes Ornstein Uhlenbeck and the Fractional Ornstein Uhlenbeck. Prognostic assessment is supported on the Diebold and Mariano test and a financial evaluation of an investment without transaction costs. Although the estimation of persistence could strengthen with inferential evidence, it's suggested also the importance of taking into account this pattern for better accuracy in forecasting and a better return on investment working with a generative process that assumes dependence instead independence.