A new estimator of the self-similarity exponent through the empirical likelihood ratio test
A new method is proposed to estimate the self-similarity exponent. Instead of applying finite moment(s) methods, a goodness-of-fit statistic is designed to test whether two rescaled sequences are drawn from the same distribution, which is the definition of self-similarity. The test is the empirical likelihood ratio, which is robust with respect to processes with dependence. We provide a closed formula for fractional Brownian motion and prove that the distance between two rescaled sequences is zero iff the scaling exponent equals the true one.