Do Macroeconomic Relationships Exhibit Multifractal Cross-Correlations? Evidence from Inflation, Unemployment and Interest Rates

This paper studies the scale-dependent co-movements of monthly changes in U.S. unemployment, inflation, and the federal funds rate from July 1954 to May 2026 using contemporaneous, lagged, and asymmetric Multifractal Detrended Cross-Correlation Analysis (MF-DCCA). Significance is assessed against 200 Iterative Amplitude Adjusted Fourier Transform (IAAFT) surrogates for every pair, lag, and trend regime, and the lead–lag patterns are compared with a linear VAR benchmark. The generalized cross-Hurst exponent Hxy(q) varies with the moment order q: the cross-scaling of small co-fluctuations (q<0) is largely compatible with the surrogate null, whereas that of moderate and large co-fluctuations departs from it at horizons of up to 12 months. The lead–lag cross-persistence between policy-rate changes and unemployment, and from policy-rate changes to inflation, is approximately invariant across horizons of 1 to 12 months, whereas for unemployment and inflation, and from inflation to policy-rate changes, the cross-persistence of large co-fluctuations increases with the horizon, most robustly from inflation to unemployment. The VAR finds linear predictability only in the first group, most robustly from policy-rate changes to inflation. The asymmetric analysis shows that joint scaling depends on the phase of the guiding series, with markedly higher cross-persistence of inflation with unemployment in high-inflation phases, a pattern that is robust to the detrending order, whereas the asymmetries involving the policy rate are less robust and the asymmetric estimates at extreme moment orders are sensitive to the estimation settings. These results are descriptive rather than structural and complement conventional macroeconometric evidence.