The small sample estimation of h

Şen Z.

Water Resources Research, vol.13, no.6, pp.971-974, 1977 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 6
  • Publication Date: 1977
  • Doi Number: 10.1029/wr013i006p00971
  • Journal Name: Water Resources Research
  • Journal Indexes: Scopus
  • Page Numbers: pp.971-974
  • Istanbul Medipol University Affiliated: No


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. Copyright 1977 by the American Geophysical Union.