ARMA Model identification of hydrologic time series

In recent years, ARMA models have become popular for modeling geophysical time series in general and hydrologic time series in particular. The identification of the appropriate order of the model is an important stage in ARMA modeling. Such model identification is generally based on the autocorrelation and partial autocorrelation functions, although recently improvements have been obtained using the inverse autocorrelation and the inverse partial autocorrelation functions. This paper demonstrates the use of the generalized partial autocorrelation function (GPAF) and the R and S functions of Gray et al. (1978) for ARMA model identification of hydrologic time series. These functions are defined, and some recursive relations are given for ease of computation. All three functions, when presented in tabular form, have certain characteristic patterns that are useful in ARMA model identification. Several examples are included to demonstrate the usefulness of the proposed identification technique. Actual applications are made using the Saint Lawrence River and Nile River annual streamflow series.