An Application of the Seasonal Fractionally Differenced Model to the Monetary Aggregates

Abstract In this article, three significant variables used by the U.S. Federal Reserve as targets to shape monetary policy, the monetary aggregates M1, M2, and M3, are examined using a seasonal fractionally differenced model. The sample autocorrelation functions of these monetary variables exhibit a decay pattern at the seasonal lags that is typical of a fractional model. The seasonal fractionally differenced model is found to remove a great deal of the autocorrelation at the seasonal lags, especially when a series is extended by splicing together earlier monetary data. Some Monte Carlo evidence as to the efficacy of this technique is presented. Finally, one-year-ahead out-of-sample forecasts of M1 are made using both the Box—Jenkins airline model and the seasonal fractionally differenced model.