Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Holder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Holder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Holder exponent can be estimated locally from discrete data in this model.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Fractional brownian motion
- Gaussian process
- Holder exponent
- Multifractional brownian motion