In this paper, we will compare two methods of forecasting a short-term time series, through several criteria such as Aic, Bic, MSE, log likelihood, j2 and other. The first one of this two methods is the popular algorithm of Box-Jenkins and the second is the exponential smoothing method. We are interested in the evolution over time of a phenomenon, in order to describe, explain and predict this phenomenon in the future. We have observations at different dates, i.e. a series of numerical values indexed by time. For this, we will use R software. R is free software and programming language. It is very powerful for statistical methods, helps us to exploit the theoretical results obtained in the analysis of time series.