||The Box-Jenkins forecasting approach has gained great popularity in the last decades. Applications can be found in many scientific fields, such as geography, economics, and demography. This paper presents the results of an investigation to assess the utility of the univariate Box-Jenkins technique for analyzing and forecasting touristic time series of Greenland between 1994 and 2015. The variables include the number of international air and cruise passengers, the number of hotel stays and guests, and the number of rented rooms. The monthly numbers show strong seasonality within each year. There is no apparent trend in the data over the chosen period. Because of the seasonality we use seasonal ARMA (autoregressive-moving average) time series models for the analysis. In a seasonal ARMA model, seasonal AR and MA terms predict forecasts at time t using data values and errors at times with lags that are multiples of 12. After the inspection of the plot, we use the sample autocorrelation function (ACF) and the sample partial autocorrelation function (PACF) to specify the order of the ARMA model. It turns out that an ARMA(2,1) specification is appropriate for most seasonally adjusted variables. In the next step the parameters of the model are estimated by nonlinear least squares. With the chosen models it is possible to make short term monthly forecasts. The residuals from the fitted model are examined to see if the selected model is appropriate. The further into the future we forecast, the more uncertain our forecasts become, as indicated by the widening of the confidence interval, at the longer lead times. Finally, Box-Jenkins forecasts are compared with the accuracy of forecasts made with other traditional time series models. The accuracy of the Box-Jenkins model is better than the accuracy of the traditional time series models.