On Long Memory Origins and Forecast Horizons

Most long memory forecasting studies assume that long memory is generated by the fractional difference operator. We argue that the most cited theoretical arguments for the presence of long memory do not imply the fractional difference operator and assess the performance of the autoregressive fractionally integrated moving average (ARFIMA) model when forecasting series with long memory generated by nonfractional models. We find that ARFIMA models dominate in forecast performance regardless of the long memory generating mechanism and forecast horizon. Nonetheless, forecasting uncertainty at the shortest forecast horizon could make short memory models provide suitable forecast performance, particularly for smaller degrees of memory. Additionally, we analyse the forecasting performance of the heterogeneous autoregressive (HAR) model, which imposes restrictions on
high-order AR models. We find that the structure imposed by the HAR model produces better short and medium horizon forecasts than unconstrained AR models of the same order. Our results have implications for, among others, Climate Econometrics and Financial Econometrics models dealing with long memory series at different forecast horizons.