What ProcessEstimator Options can I use with FractionalBrownianMotionProcess

Question

I can generate an fBm process:

tlow = 0;
thigh = 1;
len = Sqrt[thigh];
tinc = 0.01;
hurst = 0.4;
DataZ = RandomFunction[
   FractionalBrownianMotionProcess[hurst], {tlow, thigh, tinc}, 1];
dataz = Flatten[DataZ[[2, 1]]];

In the following post:

Computing the Hurst exponent or fractal dimension of fractional Brownian motion

it is described that you can use FindProcessParameters to estimate the Hurst exponent:

FindProcessParameters[dataz, FractionalBrownianMotionProcess[h]]

The documentation says that you can use the ProcessEstimator options... but it does not say which one you can use... I am guessing that such options would be similar to Box counting, Takens estimator, etc.

What are the ProcessEstimator options that can be used with FractionalBrownianMotionProcess?

Answer 1

The documentation says that you can use the ProcessEstimator options ... but it does not say which one you can use

I take exception to this statement. The documentation for FindProcessParameters clearly states two things.

• Option values Automatic, "MaximumLikelihood", and "MethodOfMoments" can be given generally as values for the option ProcessEstimator.

• Certain process functions such as HiddenMarkovProcess accept additional option values for ProcessEstimator. These are documented under the articles for such processes that do so.

Therefore, if there were addition option values for ProcessEstimator accepted by FractionalBrownianMotionProcess, they would be found in the article documenting that function. No additional values are mentioned there. Conclusion: there are no such additional option values accepted by FractionalBrownianMotionProcess unless the documentation is faulty, which is not inconceivable.