The small sample estimation of h

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Abstract
In this paper a general analytical procedure has been presented for evaluating the expected value of the Hurst coefficient h in small samples. In particular, the expectation of h has been derived analytically in an explicit form for the lag 1 Markov process, and then the validity of this analytical expression has been checked against the results obtained by Monte Carlo simulation techniques. To this end a large number of synthetic sequences have been generated for various values of sample sizes n and the lag 1 serial correlation coefficient ρ with the assumption that the underlying random variables are normally distributed. Furthermore, it has been shown that the bias in ρ for small samples is accentuated in the expected value of n which is a function of both n and ρ only.

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