The aim of this study consists in analyzing the importance of the exchange rate forecast using the Box-Jenkins models, also known as Auto Regressive Integrated Moving Average (ARIMA) models. The first part of the paper presents the main research in this field, which can be classified in two categories (studies applying classical methods, such as Box-Jenkins models and studies which rely on sophisticated prediction tools), and summarizes the main findings of some of the studies applying Box-Jenkins models. In the second part of the paper we performed a EUR/RON exchange rate analysis and forecasting, based on testing several AR, MA and ARMA candidate processes, in order to find out the best fitting model specification. We adopted the following strategy: i) an initial time series had been used for testing various model specifications, identify the best performing one and making a forecast of the EUR/RON exchange rate; ii) after comparing the accuracy of this forecast with the real level recorded by the exchange rate at end of May 2018, we conducted a second forecast, for the period September 2018 - March 2019. The initial time series employed has daily frequency and covers the timeframe July 4, 2005 - December 5, 2017, while the second time series used covers the period July 4, 2005 - August 31, 2018. The empirical findings have passed the goodness-of-fit tests and show a good predictive power. The first forecast performed for a six month period (December 2017 - May 2018) has indicated a slow pace, persistent increase of the EUR/RON exchange rate, which was confirmed by the expectations of market participants (financial analysts, banks' research departments). The second forecast, which covers the last quarter of 2018 and the first quarter of 2019, indicates a similar slow-pace rising trend. [ABSTRACT FROM AUTHOR]