IS PCA reliable for the analysis of fractional Brownian motion?

Estimation of the self-similarity parameter, also known as Hurst (H) parameter, is an important issue. In this paper, we study one of the H parameter estimation methods, namely the Principal Component Analysis (PCA) and show that this method may not give reliable results for the persistent part (H>0.5) of the fractional Brownian motion. Moreover, when the results are unreliable, the eigenvalue progression seriously deviates from linearity. Thus, with a linear-fit error threshold, one can comment on the reliability for the results of the PCA method.