Seasonal and Nonseasonal ARMA Models in Hydrology

The ARMA (autoregressive moving average) processes may be fitted to stationarized series obtained by subtraction of the seasonal means and division by the seasonal standard deviations. This standardization is effective in removing the cyclicities in the means and in the variances, but the ensemble cross-correlations are virtually unchanged. A modified family of ARMA models is presented in which the seasonality of the means, the variances, and the cross-variances are preserved. The model has seasonally varying coefficients based upon seasonally varying serial correlation coefficients. To further preserve the characteristics of the historical series, the probability distribution of the random numbers used for data generation should be similar to those of the residuals of the stochastic model. The ARMA models have been applied to 20 daily, weekly, and monthly runoff series for watersheds in the lower Ohio Basin.