I've computed multifractal spectra using MFDFA with 30 surrogate controls computed using the TISEAN surrogates routine (IAAFT surrogates). When I plot H vs q I get a mean curve for the surrogates that lies above that for the data, both curves varying with q and thus providing evidence of multifractality. If the surrogates contain monofractal noise but the data are multifractal, I would have expected no relationship between H and q for the surrogates but a monotonic decreasing relationship for the data. Similarly, the width of the multifractal spectrum is less for the data than it is for the surrogates, once again an unexpected result.

Any advice on this matter would be appreciated.