Estimates of the Hurst exponent are consistent and monotone for simulated wavelet-based fractional Brownian motion time series with Hurst exponent ranging from zero to one.

<p>Along with estimates for the simulated time series (blue), estimates for the time series integral (black) and derivative (green) are also shown. The red dotted line represents the theoretical value. Mean error is calculated as the average of the errors at each point; starred errors were computed for the derivative.