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Periodic Gamma Autoregressive Processes for Operational Hydrology
Author(s) -
Fernandez Bonifacio,
Salas Jose D.
Publication year - 1986
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr022i010p01385
Subject(s) - autoregressive model , streamflow , series (stratigraphy) , univariate , multiplicative function , mathematics , constant (computer programming) , autoregressive integrated moving average , gamma distribution , time series , autocorrelation , statistics , econometrics , multivariate statistics , computer science , geology , mathematical analysis , geography , drainage basin , paleontology , cartography , programming language
A number of models have been suggested for hydrologic time series in general and streamflow series in particular. Most of them are normal autoregressive (AR) of order 1 with either constant or periodic parameters. Since generally hydrologic time series are nonnormal (skewed), transformations have been suggested to make the series approximately normal. A new class of univariate models is proposed herein which incorporates skewed and correlation properties within the model structure without the necessity of transformations. Such models assume a gamma marginal distribution and a constant or periodic autoregressive structure. The models may be additive gamma, multiplicative gamma, or a mixed model which incorporates properties of both additive and multiplicative models. The gamma models were tested and compared in relation to (transformed) normal AR models by computer simulation studies based on five weekly streamflow series with samples varying from 35 to 40 years of record. The results show that the new class of gamma models compares favorably with respect to the normal models in reproducing the basic statistics usually analyzed for streamflow simulation. It is expected that the proposed gamma models will be of interest to other researchers for further developments and applications to hydrologic and geophysical time series.