Mathematical and Quantitative Methods

Abstract

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.