Long-Memory Forecasting of U.S. Monetary Indices

Several studies have tested for long-range dependence in macroeconomic and financial time series but very few have assessed the usefulness of long-memory models as forecast generating mechanisms. This study tests for fractional differencing in the U.S. monetary indices (simple sum and divisia) and compares the out-of-sample fractional forecasts to benchmark forecasts. The long-memory parameter is estimated using Robinson’s Gaussian semiparametric and multivariate log-periodogram methods. The evidence amply suggests that the monetary series possess a fractional order between one and two. Fractional out-of-sample forecasts are consistently more accurate (with the exception of the M3 series) than benchmark autoregressive forecasts but the forecasting gains are not generally statistically significant. In terms of forecast encompassing, the fractional model encompasses the autoregressive model for the divisia series but neither model encompasses the other for the simple sum series.