SEMIFAR Forecasts, with Applications to Foreign Exchange Rates

SEMIFAR models introduced in Beran (1999) provide a semiparametric modelling framework that enables the data analyst to separate deterministic and stochastic trends as well as short- and long-memory components in an observed time series. A correct distinction between these components, and in particular, the decision which of the components may be present in the data have an important impact on forecasts. in this paper, forecasts and forecast intervals for SEMIFAR models are obtained. The forecasts are based on an extrapolation of the stochastic component. In the data analystical part of the paper, the proposed method is applied to foreign exchange rates from Europe and Asia.