In:
Water Resources Research, American Geophysical Union (AGU), Vol. 13, No. 2 ( 1977-04), p. 281-290
Abstract:
Formulation of two models of long‐term persistence, fast fractional Gaussian noise (ffGn) and the first‐ order autoregressive‐first‐order moving average (Arma (1, 1)) process for a three‐parameter log normal and three‐parameter gamma distribution are given. For the three‐parameter log normal distribution the marginal probability distribution is generated exactly for both models, but the desired autocorrelation functions are distorted. Use of the three‐parameter log normal distribution requires a transformation of the lag one correlation coefficient and the Hurst coefficient for the ffGn model and of the parameters ϕ and θ for the Arma (1, 1) model. Because of the nonlinearity of the three‐parameter log normal transformation, sequences with slightly higher long‐term persistence (larger H or ϕ) must be generated in the logarithmic domain to achieve the desired model properties in the skewed domain. For the gamma distribution, the autocorrelation function is preserved exactly, but the desired marginal probability distribution is distorted. Monte Carlo tests showed that this distortion is evidenced primarily in the loss of the theoretical lower bound of the gamma distribution. This distortion is most extreme for time series having high long‐term persistence ( H or ϕ) and large coefficients of variation. For operational applications, there appeared to be no clear advantage to use of either of the skewed distributions.
Type of Medium:
Online Resource
ISSN:
0043-1397
,
1944-7973
DOI:
10.1029/WR013i002p00281
Language:
English
Publisher:
American Geophysical Union (AGU)
Publication Date:
1977
detail.hit.zdb_id:
2029553-4
detail.hit.zdb_id:
5564-5
SSG:
13
SSG:
14
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