Forecasting Strongly Dependent Macroeconomic and Monetary Series: A Two-Stage Approach and a Direct High-Order Autoregression

Abstract

A two step forecasting approach for long memory time series is introduced. In the first step we estimate the fractional exponent and, applying the fractional differencing operator, we obtain the underlying weakly dependent series. In the second step, we perform the multi-step ahead forecasts for the weakly dependent series and obtain their long memory counterparts by applying the fractional cumulation operator. The methodology applies to stationary and nonstationary cases. Applications to sixteen macroeconomic and monetary series indicate that the new methodology provides better forecasts. Furthermore, a high-order AR model fitted to the original data also yields to comparable results.

Keywords: Forecasting, Infinite Autoregressions, Long Memory, MLE, Local Whittle