Time series forecasting is an important type of quantitative method in which past observations of a set of variables are used to develop a model describing their relationship. The Autoregressive Integrated Moving Average (ARIMA) model is a commonly used method for modelling time series. It is applied when the data show evidence of nonstationarity, which is removed by applying an initial differencing step. Alternatively, for time series in which the long-run average decays more slowly than an exponential decay, the Autoregressive Fractionally Integrated Moving Average (ARFIMA) model is used. One important issue on time series forecasting is known as the short and long memory dependency, which corresponds to how much past history is necessary in order to make a better prediction. It is not always clear if a process is stationary or what is the influence of the past samples on the future value, and thus, which of the two models, is the best choice for a given time series. The objective of this research is to have a better understanding this dependency for an accurate prediction. Several datasets of different contexts were processed using both models, and the prediction accuracy and memory dependency were compared.