Inference on the Hurst Parameter and the Variance of Diffusions Driven by Fractional Brownian Motion by Corinne Berzin Alain Latour & José R. León

Author:Corinne Berzin, Alain Latour & José R. León
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

4.5.1.3 Confidence Intervals for H Using the Fractiles

Let us consider the optimal case with k = 2. Using these simulations results, we can give a confidence interval for H given an observed value . The idea is the following one. Suppose we would like to have a 1 −α confidence interval. Let Q β (H) be the β-fractile of the sample distribution of , i.e. Q β (H) is such that and let

To illustrate the procedure, we plotted the values of Q 0. 025(H) and Q 0. 975(H): see Fig. 4.5 .1 The points are quite close to straight lines.

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