Multifractal Modeling of the US Treasury Term Structure and Fed Funds Rate

Abstract

This paper identifies the Multifractal Models of Asset Return (MMARs) from the eight nodal term structure series of US Treasury rates as well as the Fed Funds rate and, after proper synthesis, simulates those MMARs. We show that there is an inverse persistence term structure in the sense that the short term interest rates show the highest persistence, while the long term rates are closer to the GBM's neutral persistence. The simulations of the identified MMAR are compared with the original empirical time series, but also with the simulated results from the corresponding Brownian Motion and GARCH processes. We find that the eight different maturity US Treasury and the Fed Funds rates are multifractal processes. Moreover, using wavelet scalograms, we demonstrate that the MMAR outperforms both the GBM and GARCH(1,1) in time-frequency comparisons, in particular in terms of scaling distribution preservation. Identified distributions of all simulated processes are compared with the empirical distributions in snapshot and over time-scale (frequency) analyses. The simulated MMAR can replicate all attributes of the empirical distributions, while the simulated GBM and GARCH(1,1) processes cannot preserve the thick-tails, high peaks and proper skewness. Nevertheless, the results are somewhat inconclusive when the MMAR is applied on the Fed Funds rate, which has globally a mildly anti-persistent and possibly chaotic diffusion process completely different from the other nodal term structure rates.