The maximum likelihood (ML) estimation approach for fractional Brownian motion (fBm) is explored in this communication. First, a ML based estimation of the H parameter is implemented on the signal itself. This approach on the signal itself can easily be applied on non-uniformly sampled data or directly useful in the case of incomplete data. Secondly, the method is extended to provide a ML prediction and a ML interpolation for fBm which could be of interest in many domains. Results also help to explain errors in other interpolating methods such as the midpoint displacement algorithm used to synthesize fBm data.
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