SEMIFAR Models, with Applications to Commodities, Exchange Rates and the Volatility of Stock Market Indices

The distinction between stationarity, difference stationarity, deterministic trends as well as between short- and long-range dependence has a major impact on statistical conclusions, such as confidence intervals for population quantities or point and interval forecasts. In this paper, recent results on so-called SEMIFAR models introduced by Beran(1999) are summarized and their potential usefulness for economic time series analysis is illustrated by analyzing several commodities, exchange rates, the volatility of stock market indices and some simulated series. SEMIFAR models provide a unified approach that allows for simultaneous modelling of and distinction between deterministic trends, difference stationarity and stationarity with short- and long-range dependence. An iterative data-driven algorithm combines MLE and kernel estimation. Predictions combine stochastic prediction of the random part with functional extrapolation of the deterministic part.