Barkoulas, John, Christopher Baum, and Mustafa Caglayan. “Fractional Monetary Dynamics”. Boston College Working Papers in Economics 321, 1998.
We test for fractional dynamics in U.S. monetary series, their various formulations and components, and velocity series. Using the spectral regression method, we find evidence of a fractional exponent in the differencing process of the monetary series (both simple-sum and Divisia indices), in their components (with the exception of demand deposits, savings deposits, overnight repurchase agreements, and term repurchase agreements), and the monetary base and money multipliers. No evidence of fractional behavior is found in the velocity series. Granger's (1980) aggregation hypothesis is evaluated and implications of the presence of fractional monetary dynamics are drawn.