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

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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.

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