Multifractal Modeling of the Japanese Treasury Term Structure

This paper identifies Multifractal Models of Asset Returns (MMARs) for each of the eight nodal term structure series of monthly Japanese Treasury rates and, after proper synthesis, simulates those MMARs. All nodal rate series are found to be slightly anti-persistent, with the exception of the 20-year rate which is heavily anti-persistent and in the range of being chaotic. This contrasts with our earlier findings of the US term structure (Jamdee-Los, 2005), where the US interest rates are identified to be slightly persistent, although that model identification was based on daily data. The simulations of the identified Japanese interest rate MMARs are compared with the original empirical time series, and also with the simulated results from the corresponding Geometric Brownian Motion (GBM) and GARCH processes. All eight different maturity Japanese Treasury rates are found to be multifractal processes. Identified distributions of all simulated processes are compared with the empirical distributions in both snapshot and time-scale (-frequency) analyses. Using wavelet scalograms, we demonstrate that the MMAR does not clearly outperform either the GBM and GARCH(1, 1) in time-frequency comparisons. The simulated MMAR replicates all attributes of the short maturity empirical distributions, while the simulated GBM and GARCH(1, 1) processes perform better for the long maturity series. Nevertheless, these results are somewhat inconclusive since the MMAR experiences difficulty with the simulations of these anti-persistent, and in one case, possibly chaotic, price diffusion processes