Mathematical and Quantitative Methods: Array - Collective Authors (Acta Universitatis Danubius. Œconomica, 2021)
Currency market is recently the largest world market during the existence of which there have been many theories regarding the prediction of the development of exchange rates based on macroeconomic, microeconomic, statistic and other models. The aim of this paper is to identify the adequate model for the prediction of non-stationary time series of exchange rates and then use this model to predict the trend of the development of European currencies against Euro. The uniqueness of this paper is in the fact that there are many expert studies dealing with the prediction of the currency pairs rates of the American dollar with other currency but there is only a limited number of scientific studies concerned with the long-term prediction of European currencies with the help of the integrated ARMA models even though the development of exchange rates has a crucial impact on all levels of economy and its prediction is an important indicator for individual countries, banks, companies and businessmen as well as for investors. The results of this study confirm that to predict the conditional variance and then to estimate the future values of exchange rates, it is adequate to use the ARIMA (1,1,1) model without constant, or ARIMA [(1,7),1,(1,7)] model, where in the long-term, the square root of the conditional variance inclines towards stable value.